Solve (x-3)^2=x^2+32

$$( x - 3 ) ^ { 2 } = x ^ { 2 } + 32$$

Solve for x

$$x = -\frac{23}{6} = -3\frac{5}{6} \approx -3.833333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-6x+9=x^{2}+32$$

Subtract x^{2} from both sides.

$$x^{2}-6x+9-x^{2}=32$$

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

$$-6x+9=32$$

Subtract 9 from both sides.

$$-6x=32-9$$

Subtract 9 from 32 to get 23.

$$-6x=23$$

Divide both sides by -6.

$$x=\frac{23}{-6}$$

Fraction \frac{23}{-6} can be rewritten as -\frac{23}{6} by extracting the negative sign.

$$x=-\frac{23}{6}$$