Solve x^2-left(8-xright)^2=4

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

Solve for x

$$x = \frac{17}{4} = 4\frac{1}{4} = 4.25$$

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}.

$$x^{2}-\left(64-16x+x^{2}\right)=4$$

To find the opposite of 64-16x+x^{2}, find the opposite of each term.

$$x^{2}-64+16x-x^{2}=4$$

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

$$-64+16x=4$$

Add 64 to both sides.

$$16x=4+64$$

Add 4 and 64 to get 68.

$$16x=68$$

Divide both sides by 16.

$$x=\frac{68}{16}$$

Reduce the fraction \frac{68}{16} to lowest terms by extracting and canceling out 4.

$$x=\frac{17}{4}$$