Solve Using the Quadratic Formula x^2-21=0

$x^{2} - 21 = 0$

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 $c = - 21$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 21)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 21}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 21$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 21}}{2 \cdot 1}$

Multiply $- 4$ by $- 21$ .

$x = \frac{0 \pm \sqrt{0 + 84}}{2 \cdot 1}$

Add $0$ and $84$ .

$x = \frac{0 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$x = \frac{0 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$x = \frac{0 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{0 \pm 2 \sqrt{21}}{2}$ .

$x = \pm \sqrt{21}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{21}$

Decimal Form:

$x = 4.58257569 \dots, - 4.58257569 \dots$