Use the distributive property to multiply $8$ by $x+2$.
$$\left(8x+16\right)x=0$$
Use the distributive property to multiply $8x+16$ by $x$.
$$8x^{2}+16x=0$$
Factor out $x$.
$$x\left(8x+16\right)=0$$
To find equation solutions, solve $x=0$ and $8x+16=0$.
$$x=0$$ $$x=-2$$
Steps Using the Quadratic Formula
Use the distributive property to multiply $8$ by $x+2$.
$$\left(8x+16\right)x=0$$
Use the distributive property to multiply $8x+16$ by $x$.
$$8x^{2}+16x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $8$ for $a$, $16$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{-16±\sqrt{16^{2}}}{2\times 8}$$
Take the square root of $16^{2}$.
$$x=\frac{-16±16}{2\times 8}$$
Multiply $2$ times $8$.
$$x=\frac{-16±16}{16}$$
Now solve the equation $x=\frac{-16±16}{16}$ when $±$ is plus. Add $-16$ to $16$.
$$x=\frac{0}{16}$$
Divide $0$ by $16$.
$$x=0$$
Now solve the equation $x=\frac{-16±16}{16}$ when $±$ is minus. Subtract $16$ from $-16$.
$$x=-\frac{32}{16}$$
Divide $-32$ by $16$.
$$x=-2$$
The equation is now solved.
$$x=0$$ $$x=-2$$
Steps for Completing the Square
Use the distributive property to multiply $8$ by $x+2$.
$$\left(8x+16\right)x=0$$
Use the distributive property to multiply $8x+16$ by $x$.
$$8x^{2}+16x=0$$
Divide both sides by $8$.
$$\frac{8x^{2}+16x}{8}=\frac{0}{8}$$
Dividing by $8$ undoes the multiplication by $8$.
$$x^{2}+\frac{16}{8}x=\frac{0}{8}$$
Divide $16$ by $8$.
$$x^{2}+2x=\frac{0}{8}$$
Divide $0$ by $8$.
$$x^{2}+2x=0$$
Divide $2$, the coefficient of the $x$ term, by $2$ to get $1$. Then add the square of $1$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
$$x^{2}+2x+1^{2}=1^{2}$$
Square $1$.
$$x^{2}+2x+1=1$$
Factor $x^{2}+2x+1$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.
$$\left(x+1\right)^{2}=1$$
Take the square root of both sides of the equation.
