How to solve 9x ^ 2 - 1 = 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 9x ^ 2 - 1 = 0 | Equatix

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Question

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

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

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

Add $1$ to both sides. Anything plus zero gives itself.

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

Divide both sides by $9$.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

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

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

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

Square $0$.

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

Multiply $-4$ times $9$.

$$x=\frac{0±\sqrt{-36\left(-1\right)}}{2\times 9}$$

Multiply $-36$ times $-1$.

$$x=\frac{0±\sqrt{36}}{2\times 9}$$

Take the square root of $36$.

$$x=\frac{0±6}{2\times 9}$$

Multiply $2$ times $9$.

$$x=\frac{0±6}{18}$$

Now solve the equation $x=\frac{0±6}{18}$ when $±$ is plus. Reduce the fraction $\frac{6}{18}$ to lowest terms by extracting and canceling out $6$.

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

Now solve the equation $x=\frac{0±6}{18}$ when $±$ is minus. Reduce the fraction $\frac{-6}{18}$ to lowest terms by extracting and canceling out $6$.

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

The equation is now solved.

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

Show Solution

Basic Math

Pre-Algebra

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Trigonometry

Calculus

Precalculus

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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