Solve Using the Quadratic Formula x^2=27

$x^{2} = 27$

Step 1

Subtract $27$ from both sides of the equation.

$x^{2} - 27 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 0$ , and $c = - 27$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 27)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 27}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 27$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 27}}{2 \cdot 1}$

Multiply $- 4$ by $- 27$ .

$x = \frac{0 \pm \sqrt{0 + 108}}{2 \cdot 1}$

Add $0$ and $108$ .

$x = \frac{0 \pm \sqrt{108}}{2 \cdot 1}$

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$x = \frac{0 \pm \sqrt{36 (3)}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{0 \pm \sqrt{6^{2} \cdot 3}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 6 \sqrt{3}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 6 \sqrt{3}}{2}$

Simplify $\frac{0 \pm 6 \sqrt{3}}{2}$ .

$x = \pm 3 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 3 \sqrt{3}$

Decimal Form:

$x = 5.19615242 \dots, - 5.19615242 \dots$