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

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

Solve for x

$$x=\frac{7}{8}=0.875$$

Steps for Solving Linear Equation

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

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

Subtract x^{2} from both sides.

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

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

$$16-8x=9$$

Subtract 16 from both sides.

$$-8x=9-16$$

Subtract 16 from 9 to get -7.

$$-8x=-7$$

Divide both sides by -8.

$$x=\frac{-7}{-8}$$

Fraction \frac{-7}{-8} can be simplified to \frac{7}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{8}$$