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

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

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

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}.

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

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

$$x^{2}-x^{2}-8x-16=4$$

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

$$-8x-16=4$$

Add 16 to both sides.

$$-8x=4+16$$

Add 4 and 16 to get 20.

$$-8x=20$$

Divide both sides by -8.

$$x=\frac{20}{-8}$$

Reduce the fraction \frac{20}{-8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{5}{2}$$