Solve Using the Quadratic Formula 7x^2+63=0

$7 x^{2} + 63 = 0$

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 $a = 7$ , $b = 0$ , and $c = 63$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (7 \cdot 63)}}{2 \cdot 7}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 7 \cdot 63}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot 63$ .

Multiply $- 4$ by $7$ .

$x = \frac{0 \pm \sqrt{0 - 28 \cdot 63}}{2 \cdot 7}$

Multiply $- 28$ by $63$ .

$x = \frac{0 \pm \sqrt{0 - 1764}}{2 \cdot 7}$

Subtract $1764$ from $0$ .

$x = \frac{0 \pm \sqrt{- 1764}}{2 \cdot 7}$

Rewrite $- 1764$ as $- 1 (1764)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 1764}}{2 \cdot 7}$

Rewrite $\sqrt{- 1 (1764)}$ as $\sqrt{- 1} \cdot \sqrt{1764}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{1764}}{2 \cdot 7}$

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

$x = \frac{0 \pm i \cdot \sqrt{1764}}{2 \cdot 7}$

Rewrite $1764$ as $42^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{42^{2}}}{2 \cdot 7}$

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

$x = \frac{0 \pm i \cdot 42}{2 \cdot 7}$

Move $42$ to the left of $i$ .

$x = \frac{0 \pm 42 i}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{0 \pm 42 i}{14}$

Simplify $\frac{0 \pm 42 i}{14}$ .

$x = \pm 3 i$