Solve (x-5)^2+4=x^2-7x

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

Solve for x

$$x = \frac{29}{3} = 9\frac{2}{3} \approx 9.666666667$$

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}.

$$x^{2}-10x+25+4=x^{2}-7x$$

Add 25 and 4 to get 29.

$$x^{2}-10x+29=x^{2}-7x$$

Subtract x^{2} from both sides.

$$x^{2}-10x+29-x^{2}=-7x$$

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

$$-10x+29=-7x$$

Add 7x to both sides.

$$-10x+29+7x=0$$

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

$$-3x+29=0$$

Subtract 29 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-29$$

Divide both sides by -3.

$$x=\frac{-29}{-3}$$

Fraction \frac{-29}{-3} can be simplified to \frac{29}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{29}{3}$$