How to solve k ^ 2 = - 105/32

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 k ^ 2 = - 105/32 | Equatix

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Question

$$k^{2}=\frac{-105}{32}$$

Solve for k

$k=-\frac{\sqrt{210}i}{8}\approx -0-1.811422093i$
$k=\frac{\sqrt{210}i}{8}\approx 1.811422093i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Fraction $\frac{-105}{32}$ can be rewritten as $-\frac{105}{32}$ by extracting the negative sign.

$$k^{2}=-\frac{105}{32}$$

The equation is now solved.

$$k=\frac{\sqrt{210}i}{8}$$ $$k=-\frac{\sqrt{210}i}{8}$$

Steps Using the Quadratic Formula

Fraction $\frac{-105}{32}$ can be rewritten as $-\frac{105}{32}$ by extracting the negative sign.

$$k^{2}=-\frac{105}{32}$$

Add $\frac{105}{32}$ to both sides.

$$k^{2}+\frac{105}{32}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $\frac{105}{32}$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$k=\frac{0±\sqrt{0^{2}-4\times \frac{105}{32}}}{2}$$

Square $0$.

$$k=\frac{0±\sqrt{-4\times \frac{105}{32}}}{2}$$

Multiply $-4$ times $\frac{105}{32}$.

$$k=\frac{0±\sqrt{-\frac{105}{8}}}{2}$$

Take the square root of $-\frac{105}{8}$.

$$k=\frac{0±\frac{\sqrt{210}i}{4}}{2}$$

Now solve the equation $k=\frac{0±\frac{\sqrt{210}i}{4}}{2}$ when $±$ is plus.

$$k=\frac{\sqrt{210}i}{8}$$

Now solve the equation $k=\frac{0±\frac{\sqrt{210}i}{4}}{2}$ when $±$ is minus.

$$k=-\frac{\sqrt{210}i}{8}$$

The equation is now solved.

$$k=\frac{\sqrt{210}i}{8}$$ $$k=-\frac{\sqrt{210}i}{8}$$

Show Solution

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Example

Question

Solve for k

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula