Solve 2x(x+8)=0

$$2 x ( x + 8 ) = 0$$

Solve for x

$$x=-8$$

$$x=0$$

Steps Using Factoring

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.

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

Simplify.

$$x+4=4 x+4=-4$$

Subtract 4 from both sides of the equation.

$$x=0 x=-8$$