Issolvi 2x*(x+1)+(x-2)*(2x-1/2)=(2x-1/2)^2-7/6x

$$2 x \cdot ( x + 1 ) + ( x - 2 ) \cdot ( 2 x - \frac { 1 } { 2 } ) = ( 2 x - \frac { 1 } { 2 } ) ^ { 2 } - \frac { 7 } { 6 } x$$

Solvi għal x

$$x = -\frac{9}{8} = -1\frac{1}{8} = -1.125$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 2x b'x+1.

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

Uża l-propjetà distributtiva biex timmultiplika x-2 b'2x-\frac{1}{2} u kkombina termini simili.

$$2x^{2}+2x+2x^{2}-\frac{9}{2}x+1=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

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

$$4x^{2}+2x-\frac{9}{2}x+1=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

Ikkombina 2x u -\frac{9}{2}x biex tikseb -\frac{5}{2}x.

$$4x^{2}-\frac{5}{2}x+1=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

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

$$4x^{2}-\frac{5}{2}x+1=4x^{2}-2x+\frac{1}{4}-\frac{7}{6}x$$

Ikkombina -2x u -\frac{7}{6}x biex tikseb -\frac{19}{6}x.

$$4x^{2}-\frac{5}{2}x+1=4x^{2}-\frac{19}{6}x+\frac{1}{4}$$

Naqqas 4x^{2} miż-żewġ naħat.

$$4x^{2}-\frac{5}{2}x+1-4x^{2}=-\frac{19}{6}x+\frac{1}{4}$$

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

$$-\frac{5}{2}x+1=-\frac{19}{6}x+\frac{1}{4}$$

Żid \frac{19}{6}x maż-żewġ naħat.

$$-\frac{5}{2}x+1+\frac{19}{6}x=\frac{1}{4}$$

Ikkombina -\frac{5}{2}x u \frac{19}{6}x biex tikseb \frac{2}{3}x.

$$\frac{2}{3}x+1=\frac{1}{4}$$

Naqqas 1 miż-żewġ naħat.

$$\frac{2}{3}x=\frac{1}{4}-1$$

Naqqas 1 minn \frac{1}{4} biex tikseb -\frac{3}{4}.

$$\frac{2}{3}x=-\frac{3}{4}$$

Immultiplika ż-żewġ naħat b'\frac{3}{2}, ir-reċiproku ta' \frac{2}{3}.

$$x=-\frac{3}{4}\times \frac{3}{2}$$

Immultiplika -\frac{3}{4} u \frac{3}{2} biex tikseb -\frac{9}{8}.

$$x=-\frac{9}{8}$$