Solve (x-5)^2=x^2-7x

$$( x - 5 ) ^ { 2 } = x ^ { 2 } - 7 x$$

Solve for x

$$x = \frac{25}{3} = 8\frac{1}{3} \approx 8.333333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$x^{2}-10x+25=x^{2}-7x$$

Subtract x^{2} from both sides.

$$x^{2}-10x+25-x^{2}=-7x$$

Combine x^{2} and -x^{2} to get 0.

$$-10x+25=-7x$$

Add 7x to both sides.

$$-10x+25+7x=0$$

Combine -10x and 7x to get -3x.

$$-3x+25=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-25$$

Divide both sides by -3.

$$x=\frac{-25}{-3}$$

Fraction \frac{-25}{-3} can be simplified to \frac{25}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{25}{3}$$