How to solve 16(x)^(2)=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 16(x)^(2)=9 | Equatix

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Question

$$16 { x }^{ 2 } =9$$

Solve for x

$x=\frac{3}{4}=0.75$
$x=-\frac{3}{4}=-0.75$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Divide both sides by $16$.

$$x^{2}=\frac{9}{16}$$

Subtract $\frac{9}{16}$ from both sides.

$$x^{2}-\frac{9}{16}=0$$

Multiply both sides by $16$.

$$16x^{2}-9=0$$

Consider $16x^{2}-9$. Rewrite $16x^{2}-9$ as $\left(4x\right)^{2}-3^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(4x-3\right)\left(4x+3\right)=0$$

To find equation solutions, solve $4x-3=0$ and $4x+3=0$.

$$x=\frac{3}{4}$$ $$x=-\frac{3}{4}$$

Steps by Finding Square Root

Divide both sides by $16$.

$$x^{2}=\frac{9}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{4}$$ $$x=-\frac{3}{4}$$

Steps Using the Quadratic Formula

Divide both sides by $16$.

$$x^{2}=\frac{9}{16}$$

Subtract $\frac{9}{16}$ from both sides.

$$x^{2}-\frac{9}{16}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-\frac{9}{16}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

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

Square $0$.

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

Multiply $-4$ times $-\frac{9}{16}$.

$$x=\frac{0±\sqrt{\frac{9}{4}}}{2}$$

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

$$x=\frac{0±\frac{3}{2}}{2}$$

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

$$x=\frac{3}{4}$$

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

$$x=-\frac{3}{4}$$

The equation is now solved.

$$x=\frac{3}{4}$$ $$x=-\frac{3}{4}$$

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