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

$$\frac { 5 } { 11 } \sqrt { \frac { - 5 } { 11 } }$$

Evaluate (complex solution)

$\frac{5\sqrt{55}i}{121}\approx 0.306454483i$

Solution Steps

Fraction $\frac{-5}{11}$ can be rewritten as $-\frac{5}{11}$ by extracting the negative sign.

$$\frac{5}{11}\sqrt{-\frac{5}{11}}$$

Rewrite the square root of the division $\sqrt{-\frac{5}{11}}$ as the division of square roots $\frac{\sqrt{-5}}{\sqrt{11}}$.

$$\frac{5}{11}\times \frac{\sqrt{-5}}{\sqrt{11}}$$

Factor $-5=5\left(-1\right)$. Rewrite the square root of the product $\sqrt{5\left(-1\right)}$ as the product of square roots $\sqrt{5}\sqrt{-1}$. By definition, the square root of $-1$ is $i$.

$$\frac{5}{11}\times \frac{\sqrt{5}i}{\sqrt{11}}$$

Rationalize the denominator of $\frac{\sqrt{5}i}{\sqrt{11}}$ by multiplying numerator and denominator by $\sqrt{11}$.

$$\frac{5}{11}\times \frac{\sqrt{5}i\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of $\sqrt{11}$ is $11$.

$$\frac{5}{11}\times \frac{\sqrt{5}i\sqrt{11}}{11}$$

To multiply $\sqrt{5}$ and $\sqrt{11}$, multiply the numbers under the square root.

$$\frac{5}{11}\times \frac{\sqrt{55}i}{11}$$

Divide $\sqrt{55}i$ by $11$ to get $\sqrt{55}\times \left(\frac{1}{11}i\right)$.

$$\frac{5}{11}\sqrt{55}\times \left(\frac{1}{11}i\right)$$

Multiply $\frac{5}{11}$ and $\frac{1}{11}i$ to get $\frac{5}{121}i$.

$$\frac{5}{121}i\sqrt{55}$$

Show Solution

Real Part (complex solution)

$0$

Evaluate

$\text{Indeterminate}$