Solve Using the Quadratic Formula x^2+225=0

$x^{2} + 225 = 0$

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 $c = 225$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 225)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 225}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 225$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 225}}{2 \cdot 1}$

Multiply $- 4$ by $225$ .

$x = \frac{0 \pm \sqrt{0 - 900}}{2 \cdot 1}$

Subtract $900$ from $0$ .

$x = \frac{0 \pm \sqrt{- 900}}{2 \cdot 1}$

Rewrite $- 900$ as $- 1 (900)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 900}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (900)}$ as $\sqrt{- 1} \cdot \sqrt{900}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{900}}{2 \cdot 1}$

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

$x = \frac{0 \pm i \cdot \sqrt{900}}{2 \cdot 1}$

Rewrite $900$ as $30^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{30^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm i \cdot 30}{2 \cdot 1}$

Move $30$ to the left of $i$ .

$x = \frac{0 \pm 30 i}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 30 i}{2}$

Simplify $\frac{0 \pm 30 i}{2}$ .

$x = \pm 15 i$