Issolvi 7(x-4)^2-3(x+5)^2=4(x+1)(x-1)-2

$$7 ( x - 4 ) ^ { 2 } - 3 ( x + 5 ) ^ { 2 } = 4 ( x + 1 ) ( x - 1 ) - 2$$

Solvi għal x

$$x=\frac{1}{2}=0.5$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-4\right)^{2}.

$$7\left(x^{2}-8x+16\right)-3\left(x+5\right)^{2}=4\left(x+1\right)\left(x-1\right)-2$$

Uża l-propjetà distributtiva biex timmultiplika 7 b'x^{2}-8x+16.

$$7x^{2}-56x+112-3\left(x+5\right)^{2}=4\left(x+1\right)\left(x-1\right)-2$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+5\right)^{2}.

$$7x^{2}-56x+112-3\left(x^{2}+10x+25\right)=4\left(x+1\right)\left(x-1\right)-2$$

Uża l-propjetà distributtiva biex timmultiplika -3 b'x^{2}+10x+25.

$$7x^{2}-56x+112-3x^{2}-30x-75=4\left(x+1\right)\left(x-1\right)-2$$

Ikkombina 7x^{2} u -3x^{2} biex tikseb 4x^{2}.

$$4x^{2}-56x+112-30x-75=4\left(x+1\right)\left(x-1\right)-2$$

Ikkombina -56x u -30x biex tikseb -86x.

$$4x^{2}-86x+112-75=4\left(x+1\right)\left(x-1\right)-2$$

Naqqas 75 minn 112 biex tikseb 37.

$$4x^{2}-86x+37=4\left(x+1\right)\left(x-1\right)-2$$

Uża l-propjetà distributtiva biex timmultiplika 4 b'x+1.

$$4x^{2}-86x+37=\left(4x+4\right)\left(x-1\right)-2$$

Uża l-propjetà distributtiva biex timmultiplika 4x+4 b'x-1 u kkombina termini simili.

$$4x^{2}-86x+37=4x^{2}-4-2$$

Naqqas 2 minn -4 biex tikseb -6.

$$4x^{2}-86x+37=4x^{2}-6$$

Naqqas 4x^{2} miż-żewġ naħat.

$$4x^{2}-86x+37-4x^{2}=-6$$

Ikkombina 4x^{2} u -4x^{2} biex tikseb 0.

$$-86x+37=-6$$

Naqqas 37 miż-żewġ naħat.

$$-86x=-6-37$$

Naqqas 37 minn -6 biex tikseb -43.

$$-86x=-43$$

Iddividi ż-żewġ naħat b'-86.

$$x=\frac{-43}{-86}$$

Naqqas il-frazzjoni \frac{-43}{-86} għat-termini l-aktar baxxi billi testratta u tikkanċella barra -43.

$$x=\frac{1}{2}$$