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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

Subtract 4 from 4 to get 0.

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

Swap sides so that all variable terms are on the left hand side.

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

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

$$4x=y$$

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

Solve for y

$$y=4x$$

Solution Steps

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

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

Subtract 4 from 4 to get 0.

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

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

$$y=4x$$