Solve x^2+4^2=(6-x)^2

$$x ^ { 2 } + 4 ^ { 2 } = ( 6 - x ) ^ { 2 }$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$x^{2}+16=\left(6-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-x\right)^{2}.

$$x^{2}+16=36-12x+x^{2}$$

Add 12x to both sides.

$$x^{2}+16+12x=36+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+16+12x-x^{2}=36$$

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

$$16+12x=36$$

Subtract 16 from both sides.

$$12x=36-16$$

Subtract 16 from 36 to get 20.

$$12x=20$$

Divide both sides by 12.

$$x=\frac{20}{12}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{5}{3}$$