Solve Using the Quadratic Formula x^2+47=3

$x^{2} + 47 = 3$

Step 1

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

Subtract $3$ from both sides of the equation.

$x^{2} + 47 - 3 = 0$

Subtract $3$ from $47$ .

$x^{2} + 44 = 0$

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 $c = 44$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 44)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 44}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 44$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 44}}{2 \cdot 1}$

Multiply $- 4$ by $44$ .

$x = \frac{0 \pm \sqrt{0 - 176}}{2 \cdot 1}$

Subtract $176$ from $0$ .

$x = \frac{0 \pm \sqrt{- 176}}{2 \cdot 1}$

Rewrite $- 176$ as $- 1 (176)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 176}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (176)}$ as $\sqrt{- 1} \cdot \sqrt{176}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{176}}{2 \cdot 1}$

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

$x = \frac{0 \pm i \cdot \sqrt{176}}{2 \cdot 1}$

Rewrite $176$ as $4^{2} \cdot 11$ .

Factor $16$ out of $176$ .

$x = \frac{0 \pm i \cdot \sqrt{16 (11)}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{4^{2} \cdot 11}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (4 \sqrt{11})}{2 \cdot 1}$

Move $4$ to the left of $i$ .

$x = \frac{0 \pm 4 i \sqrt{11}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 4 i \sqrt{11}}{2}$

Simplify $\frac{0 \pm 4 i \sqrt{11}}{2}$ .

$x = \pm 2 i \sqrt{11}$