Issolvi 3/2+2625+3/2/frac{x+25{2}}=300/x+frac{1}{2}

$$\frac{ 3 }{ 2 } + \frac{ 2625+ \frac{ 3 }{ 2 } }{ \frac{ x+25 }{ 2 } } = \frac{ 300 }{ x } + \frac{ 1 }{ 2 }$$

Solvi għal x (complex solution)

$$x=\sqrt{6202621}-2489\approx 1.506173451$$

$$x=-\left(\sqrt{6202621}+2489\right)\approx -4979.506173451$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2x, l-inqas denominatur komuni ta' 2,x.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{3}{2} biex tikseb 3.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Żid 2625 u \frac{3}{2} biex tikseb \frac{5253}{2}.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 4 u \frac{5253}{2} biex tikseb 10506.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u 300 biex tikseb 600.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{1}{2} biex tikseb 1.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Naqqas 600 miż-żewġ naħat.

$$3x+10506x\left(x+25\right)^{-1}-600=x$$

Naqqas x miż-żewġ naħat.

$$3x+10506x\left(x+25\right)^{-1}-600-x=0$$

Ikkombina 3x u -x biex tikseb 2x.

$$2x+10506x\left(x+25\right)^{-1}-600=0$$

Erġa' ordna t-termini.

$$2x+10506\times \frac{1}{x+25}x-600=0$$

Il-varjabbli x ma jistax ikun ugwali għal -25 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x+25.

$$2x\left(x+25\right)+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

Uża l-propjetà distributtiva biex timmultiplika 2x b'x+25.

$$2x^{2}+50x+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

Immultiplika 10506 u 1 biex tikseb 10506.

$$2x^{2}+50x+10506x+\left(x+25\right)\left(-600\right)=0$$

Ikkombina 50x u 10506x biex tikseb 10556x.

$$2x^{2}+10556x+\left(x+25\right)\left(-600\right)=0$$

Uża l-propjetà distributtiva biex timmultiplika x+25 b'-600.

$$2x^{2}+10556x-600x-15000=0$$

Ikkombina 10556x u -600x biex tikseb 9956x.

$$2x^{2}+9956x-15000=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 2 għal a, 9956 għal b, u -15000 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9956±\sqrt{9956^{2}-4\times 2\left(-15000\right)}}{2\times 2}$$

Ikkwadra 9956.

$$x=\frac{-9956±\sqrt{99121936-4\times 2\left(-15000\right)}}{2\times 2}$$

Immultiplika -4 b'2.

$$x=\frac{-9956±\sqrt{99121936-8\left(-15000\right)}}{2\times 2}$$

Immultiplika -8 b'-15000.

$$x=\frac{-9956±\sqrt{99121936+120000}}{2\times 2}$$

Żid 99121936 ma' 120000.

$$x=\frac{-9956±\sqrt{99241936}}{2\times 2}$$

Ħu l-għerq kwadrat ta' 99241936.

$$x=\frac{-9956±4\sqrt{6202621}}{2\times 2}$$

Immultiplika 2 b'2.

$$x=\frac{-9956±4\sqrt{6202621}}{4}$$

Issa solvi l-ekwazzjoni x=\frac{-9956±4\sqrt{6202621}}{4} fejn ± hija plus. Żid -9956 ma' 4\sqrt{6202621}.

$$x=\frac{4\sqrt{6202621}-9956}{4}$$

Iddividi -9956+4\sqrt{6202621} b'4.

$$x=\sqrt{6202621}-2489$$

Issa solvi l-ekwazzjoni x=\frac{-9956±4\sqrt{6202621}}{4} fejn ± hija minus. Naqqas 4\sqrt{6202621} minn -9956.

$$x=\frac{-4\sqrt{6202621}-9956}{4}$$

Iddividi -9956-4\sqrt{6202621} b'4.

$$x=-\sqrt{6202621}-2489$$

L-ekwazzjoni issa solvuta.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2x, l-inqas denominatur komuni ta' 2,x.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{3}{2} biex tikseb 3.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Żid 2625 u \frac{3}{2} biex tikseb \frac{5253}{2}.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 4 u \frac{5253}{2} biex tikseb 10506.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u 300 biex tikseb 600.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{1}{2} biex tikseb 1.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Naqqas x miż-żewġ naħat.

$$3x+10506x\left(x+25\right)^{-1}-x=600$$

Ikkombina 3x u -x biex tikseb 2x.

$$2x+10506x\left(x+25\right)^{-1}=600$$

Erġa' ordna t-termini.

$$2x+10506\times \frac{1}{x+25}x=600$$

Il-varjabbli x ma jistax ikun ugwali għal -25 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x+25.

$$2x\left(x+25\right)+10506\times 1x=600\left(x+25\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x b'x+25.

$$2x^{2}+50x+10506\times 1x=600\left(x+25\right)$$

Immultiplika 10506 u 1 biex tikseb 10506.

$$2x^{2}+50x+10506x=600\left(x+25\right)$$

Ikkombina 50x u 10506x biex tikseb 10556x.

$$2x^{2}+10556x=600\left(x+25\right)$$

Uża l-propjetà distributtiva biex timmultiplika 600 b'x+25.

$$2x^{2}+10556x=600x+15000$$

Naqqas 600x miż-żewġ naħat.

$$2x^{2}+10556x-600x=15000$$

Ikkombina 10556x u -600x biex tikseb 9956x.

$$2x^{2}+9956x=15000$$

Iddividi ż-żewġ naħat b'2.

$$\frac{2x^{2}+9956x}{2}=\frac{15000}{2}$$

Meta tiddividi b'2 titneħħa l-multiplikazzjoni b'2.

$$x^{2}+\frac{9956}{2}x=\frac{15000}{2}$$

Iddividi 9956 b'2.

$$x^{2}+4978x=\frac{15000}{2}$$

Iddividi 15000 b'2.

$$x^{2}+4978x=7500$$

Iddividi 4978, il-koeffiċjent tat-terminu x, b'2 biex tikseb 2489. Imbagħad żid il-kwadru ta' 2489 maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+4978x+2489^{2}=7500+2489^{2}$$

Ikkwadra 2489.

$$x^{2}+4978x+6195121=7500+6195121$$

Żid 7500 ma' 6195121.

$$x^{2}+4978x+6195121=6202621$$

Fattur x^{2}+4978x+6195121. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2489\right)^{2}=6202621$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(x+2489\right)^{2}}=\sqrt{6202621}$$

Issimplifika.

$$x+2489=\sqrt{6202621} x+2489=-\sqrt{6202621}$$

Naqqas 2489 miż-żewġ naħat tal-ekwazzjoni.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$

Solvi għal x

$$x=\sqrt{6202621}-2489\approx 1.506173451$$

$$x=-\sqrt{6202621}-2489\approx -4979.506173451$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2x, l-inqas denominatur komuni ta' 2,x.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{3}{2} biex tikseb 3.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Żid 2625 u \frac{3}{2} biex tikseb \frac{5253}{2}.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 4 u \frac{5253}{2} biex tikseb 10506.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u 300 biex tikseb 600.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{1}{2} biex tikseb 1.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Naqqas 600 miż-żewġ naħat.

$$3x+10506x\left(x+25\right)^{-1}-600=x$$

Naqqas x miż-żewġ naħat.

$$3x+10506x\left(x+25\right)^{-1}-600-x=0$$

Ikkombina 3x u -x biex tikseb 2x.

$$2x+10506x\left(x+25\right)^{-1}-600=0$$

Erġa' ordna t-termini.

$$2x+10506\times \frac{1}{x+25}x-600=0$$

Il-varjabbli x ma jistax ikun ugwali għal -25 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x+25.

$$2x\left(x+25\right)+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

Uża l-propjetà distributtiva biex timmultiplika 2x b'x+25.

$$2x^{2}+50x+10506\times 1x+\left(x+25\right)\left(-600\right)=0$$

Immultiplika 10506 u 1 biex tikseb 10506.

$$2x^{2}+50x+10506x+\left(x+25\right)\left(-600\right)=0$$

Ikkombina 50x u 10506x biex tikseb 10556x.

$$2x^{2}+10556x+\left(x+25\right)\left(-600\right)=0$$

Uża l-propjetà distributtiva biex timmultiplika x+25 b'-600.

$$2x^{2}+10556x-600x-15000=0$$

Ikkombina 10556x u -600x biex tikseb 9956x.

$$2x^{2}+9956x-15000=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 2 għal a, 9956 għal b, u -15000 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9956±\sqrt{9956^{2}-4\times 2\left(-15000\right)}}{2\times 2}$$

Ikkwadra 9956.

$$x=\frac{-9956±\sqrt{99121936-4\times 2\left(-15000\right)}}{2\times 2}$$

Immultiplika -4 b'2.

$$x=\frac{-9956±\sqrt{99121936-8\left(-15000\right)}}{2\times 2}$$

Immultiplika -8 b'-15000.

$$x=\frac{-9956±\sqrt{99121936+120000}}{2\times 2}$$

Żid 99121936 ma' 120000.

$$x=\frac{-9956±\sqrt{99241936}}{2\times 2}$$

Ħu l-għerq kwadrat ta' 99241936.

$$x=\frac{-9956±4\sqrt{6202621}}{2\times 2}$$

Immultiplika 2 b'2.

$$x=\frac{-9956±4\sqrt{6202621}}{4}$$

Issa solvi l-ekwazzjoni x=\frac{-9956±4\sqrt{6202621}}{4} fejn ± hija plus. Żid -9956 ma' 4\sqrt{6202621}.

$$x=\frac{4\sqrt{6202621}-9956}{4}$$

Iddividi -9956+4\sqrt{6202621} b'4.

$$x=\sqrt{6202621}-2489$$

Issa solvi l-ekwazzjoni x=\frac{-9956±4\sqrt{6202621}}{4} fejn ± hija minus. Naqqas 4\sqrt{6202621} minn -9956.

$$x=\frac{-4\sqrt{6202621}-9956}{4}$$

Iddividi -9956-4\sqrt{6202621} b'4.

$$x=-\sqrt{6202621}-2489$$

L-ekwazzjoni issa solvuta.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2x, l-inqas denominatur komuni ta' 2,x.

$$2x\times \frac{3}{2}+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{3}{2} biex tikseb 3.

$$3x+4x\left(x+25\right)^{-1}\left(2625+\frac{3}{2}\right)=2\times 300+2x\times \frac{1}{2}$$

Żid 2625 u \frac{3}{2} biex tikseb \frac{5253}{2}.

$$3x+4x\left(x+25\right)^{-1}\times \frac{5253}{2}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 4 u \frac{5253}{2} biex tikseb 10506.

$$3x+10506x\left(x+25\right)^{-1}=2\times 300+2x\times \frac{1}{2}$$

Immultiplika 2 u 300 biex tikseb 600.

$$3x+10506x\left(x+25\right)^{-1}=600+2x\times \frac{1}{2}$$

Immultiplika 2 u \frac{1}{2} biex tikseb 1.

$$3x+10506x\left(x+25\right)^{-1}=600+x$$

Naqqas x miż-żewġ naħat.

$$3x+10506x\left(x+25\right)^{-1}-x=600$$

Ikkombina 3x u -x biex tikseb 2x.

$$2x+10506x\left(x+25\right)^{-1}=600$$

Erġa' ordna t-termini.

$$2x+10506\times \frac{1}{x+25}x=600$$

Il-varjabbli x ma jistax ikun ugwali għal -25 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x+25.

$$2x\left(x+25\right)+10506\times 1x=600\left(x+25\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x b'x+25.

$$2x^{2}+50x+10506\times 1x=600\left(x+25\right)$$

Immultiplika 10506 u 1 biex tikseb 10506.

$$2x^{2}+50x+10506x=600\left(x+25\right)$$

Ikkombina 50x u 10506x biex tikseb 10556x.

$$2x^{2}+10556x=600\left(x+25\right)$$

Uża l-propjetà distributtiva biex timmultiplika 600 b'x+25.

$$2x^{2}+10556x=600x+15000$$

Naqqas 600x miż-żewġ naħat.

$$2x^{2}+10556x-600x=15000$$

Ikkombina 10556x u -600x biex tikseb 9956x.

$$2x^{2}+9956x=15000$$

Iddividi ż-żewġ naħat b'2.

$$\frac{2x^{2}+9956x}{2}=\frac{15000}{2}$$

Meta tiddividi b'2 titneħħa l-multiplikazzjoni b'2.

$$x^{2}+\frac{9956}{2}x=\frac{15000}{2}$$

Iddividi 9956 b'2.

$$x^{2}+4978x=\frac{15000}{2}$$

Iddividi 15000 b'2.

$$x^{2}+4978x=7500$$

Iddividi 4978, il-koeffiċjent tat-terminu x, b'2 biex tikseb 2489. Imbagħad żid il-kwadru ta' 2489 maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+4978x+2489^{2}=7500+2489^{2}$$

Ikkwadra 2489.

$$x^{2}+4978x+6195121=7500+6195121$$

Żid 7500 ma' 6195121.

$$x^{2}+4978x+6195121=6202621$$

Fattur x^{2}+4978x+6195121. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2489\right)^{2}=6202621$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(x+2489\right)^{2}}=\sqrt{6202621}$$

Issimplifika.

$$x+2489=\sqrt{6202621} x+2489=-\sqrt{6202621}$$

Naqqas 2489 miż-żewġ naħat tal-ekwazzjoni.

$$x=\sqrt{6202621}-2489 x=-\sqrt{6202621}-2489$$