How to solve (x)^(2)-9=13

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 (x)^(2)-9=13 | Equatix

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Question

$${ x }^{ 2 } -9=13$$

Solve for x

$x=\sqrt{22}\approx 4.69041576$
$x=-\sqrt{22}\approx -4.69041576$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $9$ to both sides.

$$x^{2}=13+9$$

Add $13$ and $9$ to get $22$.

$$x^{2}=22$$

Take the square root of both sides of the equation.

$$x=\sqrt{22}$$ $$x=-\sqrt{22}$$

Steps Using the Quadratic Formula

Subtract $13$ from both sides.

$$x^{2}-9-13=0$$

Subtract $13$ from $-9$ to get $-22$.

$$x^{2}-22=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-22$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-22\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-22\right)}}{2}$$

Multiply $-4$ times $-22$.

$$x=\frac{0±\sqrt{88}}{2}$$

Take the square root of $88$.

$$x=\frac{0±2\sqrt{22}}{2}$$

Now solve the equation $x=\frac{0±2\sqrt{22}}{2}$ when $±$ is plus.

$$x=\sqrt{22}$$

Now solve the equation $x=\frac{0±2\sqrt{22}}{2}$ when $±$ is minus.

$$x=-\sqrt{22}$$

The equation is now solved.

$$x=\sqrt{22}$$ $$x=-\sqrt{22}$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula