Issolvi 20^2+left(15tright)^2-left(12+15tright)^2/60t=frac{34^2+{left(15tright)}^2-{left(30+15tright)}^2}{-102t}

$$\frac{ { 20 }^{ 2 } + { \left(15t \right) }^{ 2 } - { \left(12+15t \right) }^{ 2 } }{ 60t } = \frac{ { 34 }^{ 2 } + { \left(15t \right) }^{ 2 } - { \left(30+15t \right) }^{ 2 } }{ -102t }$$

Solvi għal t

$$t=\frac{16}{35}\approx 0.457142857$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli t ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'1020t, l-inqas denominatur komuni ta' 60t,-102t.

$$17\left(20^{2}+\left(15t\right)^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Ikkalkula 20 bil-power ta' 2 u tikseb 400.

$$17\left(400+\left(15t\right)^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Espandi \left(15t\right)^{2}.

$$17\left(400+15^{2}t^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Ikkalkula 15 bil-power ta' 2 u tikseb 225.

$$17\left(400+225t^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(12+15t\right)^{2}.

$$17\left(400+225t^{2}-\left(144+360t+225t^{2}\right)\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Biex issib l-oppost ta' 144+360t+225t^{2}, sib l-oppost ta' kull terminu.

$$17\left(400+225t^{2}-144-360t-225t^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Naqqas 144 minn 400 biex tikseb 256.

$$17\left(256+225t^{2}-360t-225t^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Ikkombina 225t^{2} u -225t^{2} biex tikseb 0.

$$17\left(256-360t\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 17 b'256-360t.

$$4352-6120t=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Ikkalkula 34 bil-power ta' 2 u tikseb 1156.

$$4352-6120t=-10\left(1156+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Espandi \left(15t\right)^{2}.

$$4352-6120t=-10\left(1156+15^{2}t^{2}-\left(30+15t\right)^{2}\right)$$

Ikkalkula 15 bil-power ta' 2 u tikseb 225.

$$4352-6120t=-10\left(1156+225t^{2}-\left(30+15t\right)^{2}\right)$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(30+15t\right)^{2}.

$$4352-6120t=-10\left(1156+225t^{2}-\left(900+900t+225t^{2}\right)\right)$$

Biex issib l-oppost ta' 900+900t+225t^{2}, sib l-oppost ta' kull terminu.

$$4352-6120t=-10\left(1156+225t^{2}-900-900t-225t^{2}\right)$$

Naqqas 900 minn 1156 biex tikseb 256.

$$4352-6120t=-10\left(256+225t^{2}-900t-225t^{2}\right)$$

Ikkombina 225t^{2} u -225t^{2} biex tikseb 0.

$$4352-6120t=-10\left(256-900t\right)$$

Uża l-propjetà distributtiva biex timmultiplika -10 b'256-900t.

$$4352-6120t=-2560+9000t$$

Naqqas 9000t miż-żewġ naħat.

$$4352-6120t-9000t=-2560$$

Ikkombina -6120t u -9000t biex tikseb -15120t.

$$4352-15120t=-2560$$

Naqqas 4352 miż-żewġ naħat.

$$-15120t=-2560-4352$$

Naqqas 4352 minn -2560 biex tikseb -6912.

$$-15120t=-6912$$

Iddividi ż-żewġ naħat b'-15120.

$$t=\frac{-6912}{-15120}$$

Naqqas il-frazzjoni \frac{-6912}{-15120} għat-termini l-aktar baxxi billi testratta u tikkanċella barra -432.

$$t=\frac{16}{35}$$