Solve Using the Quadratic Formula 7x^2-98=0

$7 x^{2} - 98 = 0$

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

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (7 \cdot - 98)}}{2 \cdot 7}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 7 \cdot - 98}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot - 98$ .

Multiply $- 4$ by $7$ .

$x = \frac{0 \pm \sqrt{0 - 28 \cdot - 98}}{2 \cdot 7}$

Multiply $- 28$ by $- 98$ .

$x = \frac{0 \pm \sqrt{0 + 2744}}{2 \cdot 7}$

Add $0$ and $2744$ .

$x = \frac{0 \pm \sqrt{2744}}{2 \cdot 7}$

Rewrite $2744$ as $14^{2} \cdot 14$ .

Factor $196$ out of $2744$ .

$x = \frac{0 \pm \sqrt{196 (14)}}{2 \cdot 7}$

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

$x = \frac{0 \pm \sqrt{14^{2} \cdot 14}}{2 \cdot 7}$

Pull terms out from under the radical.

$x = \frac{0 \pm 14 \sqrt{14}}{2 \cdot 7}$

Multiply $2$ by $7$ .

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

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

$x = \pm \sqrt{14}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{14}$

Decimal Form:

$x = 3.74165738 \dots, - 3.74165738 \dots$