How to solve 4x ^ 2 - 9 = 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 4x ^ 2 - 9 = 0 | Equatix

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Question

$$4x^{2}-9=0$$

Solve for x

$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$
$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Consider $4x^{2}-9$. Rewrite $4x^{2}-9$ as $\left(2x\right)^{2}-3^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(2x-3\right)\left(2x+3\right)=0$$

To find equation solutions, solve $2x-3=0$ and $2x+3=0$.

$$x=\frac{3}{2}$$ $$x=-\frac{3}{2}$$

Steps by Finding Square Root

Add $9$ to both sides. Anything plus zero gives itself.

$$4x^{2}=9$$

Divide both sides by $4$.

$$x^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{2}$$ $$x=-\frac{3}{2}$$

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: $ax^{2}+bx+c=0$.

$$4x^{2}-9=0$$

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

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

Square $0$.

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

Multiply $-4$ times $4$.

$$x=\frac{0±\sqrt{-16\left(-9\right)}}{2\times 4}$$

Multiply $-16$ times $-9$.

$$x=\frac{0±\sqrt{144}}{2\times 4}$$

Take the square root of $144$.

$$x=\frac{0±12}{2\times 4}$$

Multiply $2$ times $4$.

$$x=\frac{0±12}{8}$$

Now solve the equation $x=\frac{0±12}{8}$ when $±$ is plus. Reduce the fraction $\frac{12}{8}$ to lowest terms by extracting and canceling out $4$.

$$x=\frac{3}{2}$$

Now solve the equation $x=\frac{0±12}{8}$ when $±$ is minus. Reduce the fraction $\frac{-12}{8}$ to lowest terms by extracting and canceling out $4$.

$$x=-\frac{3}{2}$$

The equation is now solved.

$$x=\frac{3}{2}$$ $$x=-\frac{3}{2}$$

Show Solution

Basic Math

Pre-Algebra

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Trigonometry

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Precalculus

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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