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.

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Question

$$7 + 25 ( 2 y + 3 ) ^ { 2 } = 0$$

Solve for y

$y=-\frac{\sqrt{7}i}{10}-\frac{3}{2}\approx -1.5-0.264575131i$
$y=\frac{\sqrt{7}i}{10}-\frac{3}{2}\approx -1.5+0.264575131i$

Steps by Finding Square Root

Subtracting $7$ from itself leaves $0$.

$$25\left(2y+3\right)^{2}=-7$$

Divide both sides by $25$.

$$\frac{25\left(2y+3\right)^{2}}{25}=-\frac{7}{25}$$

Dividing by $25$ undoes the multiplication by $25$.

$$\left(2y+3\right)^{2}=-\frac{7}{25}$$

Take the square root of both sides of the equation.

$$2y+3=\frac{\sqrt{7}i}{5}$$ $$2y+3=-\frac{\sqrt{7}i}{5}$$

Subtract $3$ from both sides of the equation.

$$2y+3-3=\frac{\sqrt{7}i}{5}-3$$ $$2y+3-3=-\frac{\sqrt{7}i}{5}-3$$

Subtracting $3$ from itself leaves $0$.

$$2y=\frac{\sqrt{7}i}{5}-3$$ $$2y=-\frac{\sqrt{7}i}{5}-3$$

Subtract $3$ from $\frac{i\sqrt{7}}{5}$.

$$2y=\frac{\sqrt{7}i}{5}-3$$

Subtract $3$ from $-\frac{i\sqrt{7}}{5}$.

$$2y=-\frac{\sqrt{7}i}{5}-3$$

Divide both sides by $2$.

$$\frac{2y}{2}=\frac{\frac{\sqrt{7}i}{5}-3}{2}$$ $$\frac{2y}{2}=\frac{-\frac{\sqrt{7}i}{5}-3}{2}$$

Dividing by $2$ undoes the multiplication by $2$.

$$y=\frac{\frac{\sqrt{7}i}{5}-3}{2}$$ $$y=\frac{-\frac{\sqrt{7}i}{5}-3}{2}$$

Divide $\frac{i\sqrt{7}}{5}-3$ by $2$.

$$y=\frac{\sqrt{7}i}{10}-\frac{3}{2}$$

Divide $-\frac{i\sqrt{7}}{5}-3$ by $2$.

$$y=-\frac{\sqrt{7}i}{10}-\frac{3}{2}$$

The equation is now solved.

$$y=\frac{\sqrt{7}i}{10}-\frac{3}{2}$$ $$y=-\frac{\sqrt{7}i}{10}-\frac{3}{2}$$

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