Solve Using the Quadratic Formula 5x^2-65=0

$5 x^{2} - 65 = 0$

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 $a = 5$ , $b = 0$ , and $c = - 65$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot - 65)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot - 65}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 65$ .

Multiply $- 4$ by $5$ .

$x = \frac{0 \pm \sqrt{0 - 20 \cdot - 65}}{2 \cdot 5}$

Multiply $- 20$ by $- 65$ .

$x = \frac{0 \pm \sqrt{0 + 1300}}{2 \cdot 5}$

Add $0$ and $1300$ .

$x = \frac{0 \pm \sqrt{1300}}{2 \cdot 5}$

Rewrite $1300$ as $10^{2} \cdot 13$ .

Factor $100$ out of $1300$ .

$x = \frac{0 \pm \sqrt{100 (13)}}{2 \cdot 5}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{0 \pm \sqrt{10^{2} \cdot 13}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{0 \pm 10 \sqrt{13}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{0 \pm 10 \sqrt{13}}{10}$

Simplify $\frac{0 \pm 10 \sqrt{13}}{10}$ .

$x = \pm \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{13}$

Decimal Form:

$x = 3.60555127 \dots, - 3.60555127 \dots$