How to solve (x)^(2)=(1)/(9)

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)=(1)/(9) | Equatix

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Question

$${ x }^{ 2 } = \frac{ 1 }{ 9 }$$

Solve for x

$x=\frac{1}{3}\approx 0.333333333$
$x=-\frac{1}{3}\approx -0.333333333$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Subtract $\frac{1}{9}$ from both sides.

$$x^{2}-\frac{1}{9}=0$$

Multiply both sides by $9$.

$$9x^{2}-1=0$$

Consider $9x^{2}-1$. Rewrite $9x^{2}-1$ as $\left(3x\right)^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(3x-1\right)\left(3x+1\right)=0$$

To find equation solutions, solve $3x-1=0$ and $3x+1=0$.

$$x=\frac{1}{3}$$ $$x=-\frac{1}{3}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{1}{3}$$ $$x=-\frac{1}{3}$$

Steps Using the Quadratic Formula

Subtract $\frac{1}{9}$ from both sides.

$$x^{2}-\frac{1}{9}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-\frac{1}{9}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{9}\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{9}\right)}}{2}$$

Multiply $-4$ times $-\frac{1}{9}$.

$$x=\frac{0±\sqrt{\frac{4}{9}}}{2}$$

Take the square root of $\frac{4}{9}$.

$$x=\frac{0±\frac{2}{3}}{2}$$

Now solve the equation $x=\frac{0±\frac{2}{3}}{2}$ when $±$ is plus.

$$x=\frac{1}{3}$$

Now solve the equation $x=\frac{0±\frac{2}{3}}{2}$ when $±$ is minus.

$$x=-\frac{1}{3}$$

The equation is now solved.

$$x=\frac{1}{3}$$ $$x=-\frac{1}{3}$$

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