Algebra Examples

$x^{2} - 5 i = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = 0$ , and $c = - 5 i$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot (- 5 i))}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot (- 5 i)}}{2 \cdot 1}$

Step 3.1.2

Multiply $- 4 \cdot 1 \cdot - 5$ .

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot (- 5 i)}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $- 5$ .

$x = \frac{0 \pm \sqrt{0 + 20 i}}{2 \cdot 1}$

Step 3.1.3

Add $0$ and $20 i$ .

$x = \frac{0 \pm \sqrt{20 i}}{2 \cdot 1}$

Step 3.1.4

Rewrite $20 i$ as $2^{2} \cdot (5 i)$ .

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Step 3.1.4.1

Factor $4$ out of $20$ .

$x = \frac{0 \pm \sqrt{4 (5) i}}{2 \cdot 1}$

Step 3.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{0 \pm \sqrt{2^{2} \cdot (5 i)}}{2 \cdot 1}$

Step 3.1.4.3

Add parentheses.

$x = \frac{0 \pm \sqrt{2^{2} \cdot (5 i)}}{2 \cdot 1}$

Step 3.1.5

Pull terms out from under the radical.

$x = \frac{0 \pm 2 \sqrt{5 i}}{2 \cdot 1}$

Step 3.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 2 \sqrt{5 i}}{2}$

Step 3.3

Simplify $\frac{0 \pm 2 \sqrt{5 i}}{2}$ .

$x = \pm \sqrt{5 i}$