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