Solve left(x-4right)^2+9=x^2

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

Solve for x

$$x = \frac{25}{8} = 3\frac{1}{8} = 3.125$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-8x+16+9=x^{2}$$

Add 16 and 9 to get 25.

$$x^{2}-8x+25=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-8x+25-x^{2}=0$$

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

$$-8x+25=0$$

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

$$-8x=-25$$

Divide both sides by -8.

$$x=\frac{-25}{-8}$$

Fraction \frac{-25}{-8} can be simplified to \frac{25}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{25}{8}$$