Solve for s s^2-8s=4

$s^{2} - 8 s = 4$

Subtract $4$ from both sides of the equation.

$s^{2} - 8 s - 4 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 8$ , and $c = - 4$ into the quadratic formula and solve for $s$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 4)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$s = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$s = \frac{8 \pm \sqrt{64 - 4 \cdot - 4}}{2 \cdot 1}$

Multiply $- 4$ by $- 4$ .

$s = \frac{8 \pm \sqrt{64 + 16}}{2 \cdot 1}$

Add $64$ and $16$ .

$s = \frac{8 \pm \sqrt{80}}{2 \cdot 1}$

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

Factor $16$ out of $80$ .

$s = \frac{8 \pm \sqrt{16 (5)}}{2 \cdot 1}$

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

$s = \frac{8 \pm \sqrt{4^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$s = \frac{8 \pm 4 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$s = \frac{8 \pm 4 \sqrt{5}}{2}$

Simplify $\frac{8 \pm 4 \sqrt{5}}{2}$ .

$s = 4 \pm 2 \sqrt{5}$

The final answer is the combination of both solutions.

$s = 4 + 2 \sqrt{5}, 4 - 2 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$s = 4 + 2 \sqrt{5}, 4 - 2 \sqrt{5}$

Decimal Form:

$s = 8.47213595 \dots, - 0.47213595 \dots$