Solve 9+x^2=left(x-4right)^2+20

$$9+ { x }^{ 2 } = { \left(x-4 \right) }^{ 2 } +20$$

Solve for x

$$x = \frac{27}{8} = 3\frac{3}{8} = 3.375$$

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}.

$$9+x^{2}=x^{2}-8x+16+20$$

Add 16 and 20 to get 36.

$$9+x^{2}=x^{2}-8x+36$$

Subtract x^{2} from both sides.

$$9+x^{2}-x^{2}=-8x+36$$

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

$$9=-8x+36$$

Swap sides so that all variable terms are on the left hand side.

$$-8x+36=9$$

Subtract 36 from both sides.

$$-8x=9-36$$

Subtract 36 from 9 to get -27.

$$-8x=-27$$

Divide both sides by -8.

$$x=\frac{-27}{-8}$$

Fraction \frac{-27}{-8} can be simplified to \frac{27}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{27}{8}$$