How to solve 3(x)^(2)-4=28

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 3(x)^(2)-4=28 | Equatix

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Question

$$3 { x }^{ 2 } -4=28$$

Solve for x

$x = \frac{4 \sqrt{6}}{3} \approx 3.265986324$
$x = -\frac{4 \sqrt{6}}{3} \approx -3.265986324$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $4$ to both sides.

$$3x^{2}=28+4$$

Add $28$ and $4$ to get $32$.

$$3x^{2}=32$$

Divide both sides by $3$.

$$x^{2}=\frac{32}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{6}}{3}$$ $$x=-\frac{4\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract $28$ from both sides.

$$3x^{2}-4-28=0$$

Subtract $28$ from $-4$ to get $-32$.

$$3x^{2}-32=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $3$ for $a$, $0$ for $b$, and $-32$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-32\right)}}{2\times 3}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 3\left(-32\right)}}{2\times 3}$$

Multiply $-4$ times $3$.

$$x=\frac{0±\sqrt{-12\left(-32\right)}}{2\times 3}$$

Multiply $-12$ times $-32$.

$$x=\frac{0±\sqrt{384}}{2\times 3}$$

Take the square root of $384$.

$$x=\frac{0±8\sqrt{6}}{2\times 3}$$

Multiply $2$ times $3$.

$$x=\frac{0±8\sqrt{6}}{6}$$

Now solve the equation $x=\frac{0±8\sqrt{6}}{6}$ when $±$ is plus.

$$x=\frac{4\sqrt{6}}{3}$$

Now solve the equation $x=\frac{0±8\sqrt{6}}{6}$ when $±$ is minus.

$$x=-\frac{4\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{4\sqrt{6}}{3}$$ $$x=-\frac{4\sqrt{6}}{3}$$

Show Solution

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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