Solve x^2-left(x-2right)^2=4^2

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

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

To find the opposite of x^{2}-4x+4, find the opposite of each term.

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

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

$$4x-4=4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$4x-4=16$$

Add 4 to both sides.

$$4x=16+4$$

Add 16 and 4 to get 20.

$$4x=20$$

Divide both sides by 4.

$$x=\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$x=5$$