Solve x^2+2^2=left(8-xright)^2

$${ x }^{ 2 } + { 2 }^{ 2 } = { \left(8-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

$$x^{2}+4=\left(8-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(8-x\right)^{2}.

$$x^{2}+4=64-16x+x^{2}$$

Add 16x to both sides.

$$x^{2}+4+16x=64+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+4+16x-x^{2}=64$$

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

$$4+16x=64$$

Subtract 4 from both sides.

$$16x=64-4$$

Subtract 4 from 64 to get 60.

$$16x=60$$

Divide both sides by 16.

$$x=\frac{60}{16}$$

Reduce the fraction \frac{60}{16} to lowest terms by extracting and canceling out 4.

$$x=\frac{15}{4}$$