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

$$\frac { ( x - 2 ) ^ { 2 } } { 3 } - \frac { 5 x + 1 } { 2 } = \frac { ( x - 2 ) ( x + 2 ) } { 3 }$$

Solvi għal x

$$x=\frac{13}{23}\approx 0.565217391$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'6, l-inqas denominatur komuni ta' 3,2.

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

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

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

Uża l-propjetà distributtiva biex timmultiplika 2 b'x^{2}-4x+4.

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

Uża l-propjetà distributtiva biex timmultiplika -3 b'5x+1.

$$2x^{2}-8x+8-15x-3=2\left(x-2\right)\left(x+2\right)$$

Ikkombina -8x u -15x biex tikseb -23x.

$$2x^{2}-23x+8-3=2\left(x-2\right)\left(x+2\right)$$

Naqqas 3 minn 8 biex tikseb 5.

$$2x^{2}-23x+5=2\left(x-2\right)\left(x+2\right)$$

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

$$2x^{2}-23x+5=\left(2x-4\right)\left(x+2\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2x-4 b'x+2 u kkombina termini simili.

$$2x^{2}-23x+5=2x^{2}-8$$

Naqqas 2x^{2} miż-żewġ naħat.

$$2x^{2}-23x+5-2x^{2}=-8$$

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

$$-23x+5=-8$$

Naqqas 5 miż-żewġ naħat.

$$-23x=-8-5$$

Naqqas 5 minn -8 biex tikseb -13.

$$-23x=-13$$

Iddividi ż-żewġ naħat b'-23.

$$x=\frac{-13}{-23}$$

Frazzjoni \frac{-13}{-23} tista' tiġi ssimplifikata għal \frac{13}{23} bit-tneħħija tas-sinjal negattiv min-numeratur u d-denominatur.

$$x=\frac{13}{23}$$