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

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

Solvi għal x

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 2x-1 b'1+2x u kkombina termini simili.

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

Uża l-propjetà distributtiva biex timmultiplika 3 b'x+2.

$$4x^{2}-1+\left(3x+6\right)\left(x-2\right)=7\left(x-1\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 3x+6 b'x-2 u kkombina termini simili.

$$4x^{2}-1+3x^{2}-12=7\left(x-1\right)^{2}$$

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

$$7x^{2}-1-12=7\left(x-1\right)^{2}$$

Naqqas 12 minn -1 biex tikseb -13.

$$7x^{2}-13=7\left(x-1\right)^{2}$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

$$7x^{2}-13=7\left(x^{2}-2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 7 b'x^{2}-2x+1.

$$7x^{2}-13=7x^{2}-14x+7$$

Naqqas 7x^{2} miż-żewġ naħat.

$$7x^{2}-13-7x^{2}=-14x+7$$

Ikkombina 7x^{2} u -7x^{2} biex tikseb 0.

$$-13=-14x+7$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$-14x+7=-13$$

Naqqas 7 miż-żewġ naħat.

$$-14x=-13-7$$

Naqqas 7 minn -13 biex tikseb -20.

$$-14x=-20$$

Iddividi ż-żewġ naħat b'-14.

$$x=\frac{-20}{-14}$$

Naqqas il-frazzjoni \frac{-20}{-14} għat-termini l-aktar baxxi billi testratta u tikkanċella barra -2.

$$x=\frac{10}{7}$$