How to solve 3r ^ 2 = 18

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 3r ^ 2 = 18 | Equatix

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Question

$$3r^{2}=18$$

Solve for r

$r=\sqrt{6}\approx 2.449489743$
$r=-\sqrt{6}\approx -2.449489743$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Divide both sides by $3$.

$$r^{2}=\frac{18}{3}$$

Divide $18$ by $3$ to get $6$.

$$r^{2}=6$$

Take the square root of both sides of the equation.

$$r=\sqrt{6}$$ $$r=-\sqrt{6}$$

Steps Using the Quadratic Formula

Divide both sides by $3$.

$$r^{2}=\frac{18}{3}$$

Divide $18$ by $3$ to get $6$.

$$r^{2}=6$$

Subtract $6$ from both sides.

$$r^{2}-6=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-6$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$r=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Square $0$.

$$r=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Multiply $-4$ times $-6$.

$$r=\frac{0±\sqrt{24}}{2}$$

Take the square root of $24$.

$$r=\frac{0±2\sqrt{6}}{2}$$

Now solve the equation $r=\frac{0±2\sqrt{6}}{2}$ when $±$ is plus.

$$r=\sqrt{6}$$

Now solve the equation $r=\frac{0±2\sqrt{6}}{2}$ when $±$ is minus.

$$r=-\sqrt{6}$$

The equation is now solved.

$$r=\sqrt{6}$$ $$r=-\sqrt{6}$$

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Example

Question

Solve for r

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula