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 +1650 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$2 y ^ { 2 } + 16 = 0$$

Solve for y

$y=-2\sqrt{2}i\approx -0-2.828427125i$
$y=2\sqrt{2}i\approx 2.828427125i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $16$ from both sides. Anything subtracted from zero gives its negation.

$$2y^{2}=-16$$

Divide both sides by $2$.

$$y^{2}=\frac{-16}{2}$$

Divide $-16$ by $2$ to get $-8$.

$$y^{2}=-8$$

The equation is now solved.

$$y=2\sqrt{2}i$$ $$y=-2\sqrt{2}i$$

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

$$2y^{2}+16=0$$

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

$$y=\frac{0±\sqrt{0^{2}-4\times 2\times 16}}{2\times 2}$$

Square $0$.

$$y=\frac{0±\sqrt{-4\times 2\times 16}}{2\times 2}$$

Multiply $-4$ times $2$.

$$y=\frac{0±\sqrt{-8\times 16}}{2\times 2}$$

Multiply $-8$ times $16$.

$$y=\frac{0±\sqrt{-128}}{2\times 2}$$

Take the square root of $-128$.

$$y=\frac{0±8\sqrt{2}i}{2\times 2}$$

Multiply $2$ times $2$.

$$y=\frac{0±8\sqrt{2}i}{4}$$

Now solve the equation $y=\frac{0±8\sqrt{2}i}{4}$ when $±$ is plus.

$$y=2\sqrt{2}i$$

Now solve the equation $y=\frac{0±8\sqrt{2}i}{4}$ when $±$ is minus.

$$y=-2\sqrt{2}i$$

The equation is now solved.

$$y=2\sqrt{2}i$$ $$y=-2\sqrt{2}i$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for y

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula