How to solve Equation 8 0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve Equation 8 0 | Equatix

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Question

$$\left. \begin{array} { l } { 2 x ( x + 8 ) = 0 } \end{array} \right.$$

Solve for x

$x=-8$
$x=0$

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

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.

$$x=0$$ $$x=-8$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

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Linear Algebra

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Example

Question

Solve for x

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square