Solve Using the Quadratic Formula x^2+125=0

$x^{2} + 125 = 0$

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 $c = 125$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 125)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 125}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 125$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 125}}{2 \cdot 1}$

Multiply $- 4$ by $125$ .

$x = \frac{0 \pm \sqrt{0 - 500}}{2 \cdot 1}$

Subtract $500$ from $0$ .

$x = \frac{0 \pm \sqrt{- 500}}{2 \cdot 1}$

Rewrite $- 500$ as $- 1 (500)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 500}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (500)}$ as $\sqrt{- 1} \cdot \sqrt{500}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{500}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{0 \pm i \cdot \sqrt{500}}{2 \cdot 1}$

Rewrite $500$ as $10^{2} \cdot 5$ .

Factor $100$ out of $500$ .

$x = \frac{0 \pm i \cdot \sqrt{100 (5)}}{2 \cdot 1}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{10^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (10 \sqrt{5})}{2 \cdot 1}$

Move $10$ to the left of $i$ .

$x = \frac{0 \pm 10 i \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 10 i \sqrt{5}}{2}$

Simplify $\frac{0 \pm 10 i \sqrt{5}}{2}$ .

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