Solve Using the Quadratic Formula x^2-19=0

$x^{2} - 19 = 0$

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 $c = - 19$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 19)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 19}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 19$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 19}}{2 \cdot 1}$

Multiply $- 4$ by $- 19$ .

$x = \frac{0 \pm \sqrt{0 + 76}}{2 \cdot 1}$

Add $0$ and $76$ .

$x = \frac{0 \pm \sqrt{76}}{2 \cdot 1}$

Rewrite $76$ as $2^{2} \cdot 19$ .

Factor $4$ out of $76$ .

$x = \frac{0 \pm \sqrt{4 (19)}}{2 \cdot 1}$

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

$x = \frac{0 \pm \sqrt{2^{2} \cdot 19}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 2 \sqrt{19}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 2 \sqrt{19}}{2}$

Simplify $\frac{0 \pm 2 \sqrt{19}}{2}$ .

$x = \pm \sqrt{19}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{19}$

Decimal Form:

$x = 4.35889894 \dots, - 4.35889894 \dots$