Solve Using the Quadratic Formula 49=x^2

$49 = x^{2}$

Subtract $x^{2}$ from both sides of the equation.

$49 - x^{2} = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 1$ , $b = 0$ , and $c = 49$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 49)}}{2 \cdot - 1}$

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 49}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot 49}}{2 \cdot - 1}$

Multiply $4$ by $49$ .

$x = \frac{0 \pm \sqrt{0 + 196}}{2 \cdot - 1}$

Add $0$ and $196$ .

$x = \frac{0 \pm \sqrt{196}}{2 \cdot - 1}$

Rewrite $196$ as $14^{2}$ .

$x = \frac{0 \pm \sqrt{14^{2}}}{2 \cdot - 1}$

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

$x = \frac{0 \pm 14}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{0 \pm 14}{- 2}$

Simplify $\frac{0 \pm 14}{- 2}$ .

$x = \pm 7$

The final answer is the combination of both solutions.

$x = 7, - 7$