How to solve P/2P+6=3/8

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 P/2P+6=3/8 | Equatix

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Question

$$P/2P+6=3/8$$

Solve for P

$P=-\frac{3\sqrt{5}i}{2}\approx -0-3.354101966i$
$P=\frac{3\sqrt{5}i}{2}\approx 3.354101966i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply both sides of the equation by $8$, the least common multiple of $2,8$.

$$4PP+48=3$$

Multiply $P$ and $P$ to get $P^{2}$.

$$4P^{2}+48=3$$

Subtract $48$ from both sides.

$$4P^{2}=3-48$$

Subtract $48$ from $3$ to get $-45$.

$$4P^{2}=-45$$

Divide both sides by $4$.

$$P^{2}=-\frac{45}{4}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by $8$, the least common multiple of $2,8$.

$$4PP+48=3$$

Multiply $P$ and $P$ to get $P^{2}$.

$$4P^{2}+48=3$$

Subtract $3$ from both sides.

$$4P^{2}+48-3=0$$

Subtract $3$ from $48$ to get $45$.

$$4P^{2}+45=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $4$ for $a$, $0$ for $b$, and $45$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$P=\frac{0±\sqrt{0^{2}-4\times 4\times 45}}{2\times 4}$$

Square $0$.

$$P=\frac{0±\sqrt{-4\times 4\times 45}}{2\times 4}$$

Multiply $-4$ times $4$.

$$P=\frac{0±\sqrt{-16\times 45}}{2\times 4}$$

Multiply $-16$ times $45$.

$$P=\frac{0±\sqrt{-720}}{2\times 4}$$

Take the square root of $-720$.

$$P=\frac{0±12\sqrt{5}i}{2\times 4}$$

Multiply $2$ times $4$.

$$P=\frac{0±12\sqrt{5}i}{8}$$

Now solve the equation $P=\frac{0±12\sqrt{5}i}{8}$ when $±$ is plus.

$$P=\frac{3\sqrt{5}i}{2}$$

Now solve the equation $P=\frac{0±12\sqrt{5}i}{8}$ when $±$ is minus.

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

The equation is now solved.

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

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Example

Question

Solve for P

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula