Solve Using the Quadratic Formula 98-x^2=0

$98 - x^{2} = 0$

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 $c = 98$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot 98)}}{2 \cdot - 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot 98}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 98$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot 98}}{2 \cdot - 1}$

Multiply $4$ by $98$ .

$x = \frac{0 \pm \sqrt{0 + 392}}{2 \cdot - 1}$

Add $0$ and $392$ .

$x = \frac{0 \pm \sqrt{392}}{2 \cdot - 1}$

Rewrite $392$ as $14^{2} \cdot 2$ .

Factor $196$ out of $392$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

$x = \pm 7 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm 7 \sqrt{2}$

Decimal Form:

$x = 9.89949493 \dots, - 9.89949493 \dots$