How to solve 3 ) ( - 4 )

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 3 ) ( - 4 ) | Equatix

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Question

$$( x + 3 ) ( x - 4 ) - 52 = - x$$

Solve for x

$x=-8$
$x=8$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Use the distributive property to multiply $x+3$ by $x-4$ and combine like terms.

$$x^{2}-x-12-52=-x$$

Subtract $52$ from $-12$ to get $-64$.

$$x^{2}-x-64=-x$$

Add $x$ to both sides.

$$x^{2}-x-64+x=0$$

Combine $-x$ and $x$ to get $0$.

$$x^{2}-64=0$$

Consider $x^{2}-64$. Rewrite $x^{2}-64$ as $x^{2}-8^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(x-8\right)\left(x+8\right)=0$$

To find equation solutions, solve $x-8=0$ and $x+8=0$.

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

Steps by Finding Square Root

Use the distributive property to multiply $x+3$ by $x-4$ and combine like terms.

$$x^{2}-x-12-52=-x$$

Subtract $52$ from $-12$ to get $-64$.

$$x^{2}-x-64=-x$$

Add $x$ to both sides.

$$x^{2}-x-64+x=0$$

Combine $-x$ and $x$ to get $0$.

$$x^{2}-64=0$$

Add $64$ to both sides. Anything plus zero gives itself.

$$x^{2}=64$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Use the distributive property to multiply $x+3$ by $x-4$ and combine like terms.

$$x^{2}-x-12-52=-x$$

Subtract $52$ from $-12$ to get $-64$.

$$x^{2}-x-64=-x$$

Add $x$ to both sides.

$$x^{2}-x-64+x=0$$

Combine $-x$ and $x$ to get $0$.

$$x^{2}-64=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-64$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$

Multiply $-4$ times $-64$.

$$x=\frac{0±\sqrt{256}}{2}$$

Take the square root of $256$.

$$x=\frac{0±16}{2}$$

Now solve the equation $x=\frac{0±16}{2}$ when $±$ is plus. Divide $16$ by $2$.

$$x=8$$

Now solve the equation $x=\frac{0±16}{2}$ when $±$ is minus. Divide $-16$ by $2$.

$$x=-8$$

The equation is now solved.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula