Solve Using the Quadratic Formula 5-x^2=20

$5 - x^{2} = 20$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $20$ from both sides of the equation.

$5 - x^{2} - 20 = 0$

Subtract $20$ from $5$ .

$- x^{2} - 15 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = - 1$ , $b = 0$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot - 15)}}{2 \cdot - 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot - 15}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot - 15$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot - 15}}{2 \cdot - 1}$

Multiply $4$ by $- 15$ .

$x = \frac{0 \pm \sqrt{0 - 60}}{2 \cdot - 1}$

Subtract $60$ from $0$ .

$x = \frac{0 \pm \sqrt{- 60}}{2 \cdot - 1}$

Rewrite $- 60$ as $- 1 (60)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 60}}{2 \cdot - 1}$

Rewrite $\sqrt{- 1 (60)}$ as $\sqrt{- 1} \cdot \sqrt{60}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{60}}{2 \cdot - 1}$

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

$x = \frac{0 \pm i \cdot \sqrt{60}}{2 \cdot - 1}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$x = \frac{0 \pm i \cdot \sqrt{4 (15)}}{2 \cdot - 1}$

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

$x = \frac{0 \pm i \cdot \sqrt{2^{2} \cdot 15}}{2 \cdot - 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (2 \sqrt{15})}{2 \cdot - 1}$

Move $2$ to the left of $i$ .

$x = \frac{0 \pm 2 i \sqrt{15}}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{0 \pm 2 i \sqrt{15}}{- 2}$

Simplify $\frac{0 \pm 2 i \sqrt{15}}{- 2}$ .

$x = \pm i \sqrt{15}$