165,000=d(1-(1+.002/12))^-(30)(12)/(frac{0.08{12})} を解きます| Microsoft 数学ソルバー

$$165,000 = \frac { d ( 1 - ( 1 + \frac { .002 } { 12 } ) ) ^ { - ( 30 ) ( 12 ) } } { ( \frac { 0.08 } { 12 } ) }$$

d を解く

$$d=\frac{11}{136285652597652400633072146943255896341029201131980190548843315311006893267249227122863590367756090838736813150399831954741580003320794103238355908174878733366334155884618443998783841969103173072216240445102125485099344220416740519344692695598710475488518829182397045850190391541760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 8.071282479 \cdot 10^{-1358}$$

線形方程式を解くための手順

分母と分子の両方に 1000 を乗算して、\frac{0.002}{12} を展開します。

$$165000=\frac{d\left(1-\left(1+\frac{2}{12000}\right)\right)^{-30\times 12}}{\frac{0.08}{12}}$$

2 を開いて消去して、分数 \frac{2}{12000} を約分します。

$$165000=\frac{d\left(1-\left(1+\frac{1}{6000}\right)\right)^{-30\times 12}}{\frac{0.08}{12}}$$

1 と \frac{1}{6000} を加算して \frac{6001}{6000} を求めます。

$$165000=\frac{d\left(1-\frac{6001}{6000}\right)^{-30\times 12}}{\frac{0.08}{12}}$$

1 から \frac{6001}{6000} を減算して -\frac{1}{6000} を求めます。

$$165000=\frac{d\left(-\frac{1}{6000}\right)^{-30\times 12}}{\frac{0.08}{12}}$$

-30 と 12 を乗算して -360 を求めます。

$$165000=\frac{d\left(-\frac{1}{6000}\right)^{-360}}{\frac{0.08}{12}}$$

-\frac{1}{6000} の -360 乗を計算して 13628565259765240063307214694325589634102920113198019054884331531100689326724922712286359036775609083873681315039983195474158000332079410323835590817487873336633415588461844399878384196910317307221624044510212548509934422041674051934469269559871047548851882918239704585019039154176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 を求めます。

$$165000=\frac{d\times 13628565259765240063307214694325589634102920113198019054884331531100689326724922712286359036775609083873681315039983195474158000332079410323835590817487873336633415588461844399878384196910317307221624044510212548509934422041674051934469269559871047548851882918239704585019039154176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{\frac{0.08}{12}}$$

分母と分子の両方に 100 を乗算して、\frac{0.08}{12} を展開します。

$$165000=\frac{d\times 13628565259765240063307214694325589634102920113198019054884331531100689326724922712286359036775609083873681315039983195474158000332079410323835590817487873336633415588461844399878384196910317307221624044510212548509934422041674051934469269559871047548851882918239704585019039154176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{\frac{8}{1200}}$$

8 を開いて消去して、分数 \frac{8}{1200} を約分します。

$$165000=\frac{d\times 13628565259765240063307214694325589634102920113198019054884331531100689326724922712286359036775609083873681315039983195474158000332079410323835590817487873336633415588461844399878384196910317307221624044510212548509934422041674051934469269559871047548851882918239704585019039154176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{\frac{1}{150}}$$

d\times 13628565259765240063307214694325589634102920113198019054884331531100689326724922712286359036775609083873681315039983195474158000332079410323835590817487873336633415588461844399878384196910317307221624044510212548509934422041674051934469269559871047548851882918239704585019039154176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 を \frac{1}{150} で除算して d\times 2044284788964786009496082204148838445115438016979702858232649729665103399008738406842953855516341362581052197255997479321123700049811911548575338622623181000495012338269276659981757629536547596083243606676531882276490163306251107790170390433980657132327782437735955687752855873126400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 を求めます。

$$165000=d\times 2044284788964786009496082204148838445115438016979702858232649729665103399008738406842953855516341362581052197255997479321123700049811911548575338622623181000495012338269276659981757629536547596083243606676531882276490163306251107790170390433980657132327782437735955687752855873126400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

すべての変数項が左辺にくるように辺を入れ替えます。

$$d\times 2044284788964786009496082204148838445115438016979702858232649729665103399008738406842953855516341362581052197255997479321123700049811911548575338622623181000495012338269276659981757629536547596083243606676531882276490163306251107790170390433980657132327782437735955687752855873126400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000=165000$$

両辺を 2044284788964786009496082204148838445115438016979702858232649729665103399008738406842953855516341362581052197255997479321123700049811911548575338622623181000495012338269276659981757629536547596083243606676531882276490163306251107790170390433980657132327782437735955687752855873126400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 で除算します。

$$d=\frac{165000}{2044284788964786009496082204148838445115438016979702858232649729665103399008738406842953855516341362581052197255997479321123700049811911548575338622623181000495012338269276659981757629536547596083243606676531882276490163306251107790170390433980657132327782437735955687752855873126400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

15000 を開いて消去して、分数 \frac{165000}{2044284788964786009496082204148838445115438016979702858232649729665103399008738406842953855516341362581052197255997479321123700049811911548575338622623181000495012338269276659981757629536547596083243606676531882276490163306251107790170390433980657132327782437735955687752855873126400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} を約分します。

$$d=\frac{11}{136285652597652400633072146943255896341029201131980190548843315311006893267249227122863590367756090838736813150399831954741580003320794103238355908174878733366334155884618443998783841969103173072216240445102125485099344220416740519344692695598710475488518829182397045850190391541760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$