Solve Using the Quadratic Formula x^2+8=28

$x^{2} + 8 = 28$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $28$ from both sides of the equation.

$x^{2} + 8 - 28 = 0$

Subtract $28$ from $8$ .

$x^{2} - 20 = 0$

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 $c = - 20$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 20)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 20}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 20$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 20}}{2 \cdot 1}$

Multiply $- 4$ by $- 20$ .

$x = \frac{0 \pm \sqrt{0 + 80}}{2 \cdot 1}$

Add $0$ and $80$ .

$x = \frac{0 \pm \sqrt{80}}{2 \cdot 1}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$x = \frac{0 \pm \sqrt{16 (5)}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

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

Simplify $\frac{0 \pm 4 \sqrt{5}}{2}$ .

$x = \pm 2 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{5}$

Decimal Form:

$x = 4.47213595 \dots, - 4.47213595 \dots$