Solve 36+x^2=left(8-xright)^2

$$36+ { x }^{ 2 } = { \left(8-x \right) }^{ 2 }$$

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

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

$$36+x^{2}=64-16x+x^{2}$$

Add 16x to both sides.

$$36+x^{2}+16x=64+x^{2}$$

Subtract x^{2} from both sides.

$$36+x^{2}+16x-x^{2}=64$$

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

$$36+16x=64$$

Subtract 36 from both sides.

$$16x=64-36$$

Subtract 36 from 64 to get 28.

$$16x=28$$

Divide both sides by 16.

$$x=\frac{28}{16}$$

Reduce the fraction \frac{28}{16} to lowest terms by extracting and canceling out 4.

$$x=\frac{7}{4}$$