Solve x^2-(x-4)^2=(4sqrt{3})^2

$$x ^ { 2 } - ( x - 4 ) ^ { 2 } = ( 4 \sqrt { 3 } ) ^ { 2 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-\left(x^{2}-8x+16\right)=\left(4\sqrt{3}\right)^{2}$$

To find the opposite of x^{2}-8x+16, find the opposite of each term.

$$x^{2}-x^{2}+8x-16=\left(4\sqrt{3}\right)^{2}$$

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

$$8x-16=\left(4\sqrt{3}\right)^{2}$$

Expand \left(4\sqrt{3}\right)^{2}.

$$8x-16=4^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$8x-16=16\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$8x-16=16\times 3$$

Multiply 16 and 3 to get 48.

$$8x-16=48$$

Add 16 to both sides.

$$8x=48+16$$

Add 48 and 16 to get 64.

$$8x=64$$

Divide both sides by 8.

$$x=\frac{64}{8}$$

Divide 64 by 8 to get 8.

$$x=8$$