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

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

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

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

Calculate 6 to the power of 2 and get 36.

$$16-x^{2}=36-\left(6-x\right)^{2}$$

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

$$16-x^{2}=36-\left(36-12x+x^{2}\right)$$

To find the opposite of 36-12x+x^{2}, find the opposite of each term.

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

Subtract 36 from 36 to get 0.

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

Subtract 12x from both sides.

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

Add x^{2} to both sides.

$$16-x^{2}-12x+x^{2}=0$$

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

$$16-12x=0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$-12x=-16$$

Divide both sides by -12.

$$x=\frac{-16}{-12}$$

Reduce the fraction \frac{-16}{-12} to lowest terms by extracting and canceling out -4.

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