Solve Using the Quadratic Formula x=(-(-2)+- square root of (-2)^2-41-8)/(2(1))

$x = \frac{- (- 2) + - \sqrt{{(- 2)}^{2} - 4 \cdot 1 \cdot - 8}}{2 (1)}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

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

Step 2

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

Simplify the right side.

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

Simplify the numerator.

Multiply $- 1$ by $- 2$ .

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

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

$x = \frac{2 - \sqrt{4 - 4 \cdot 1 \cdot - 8}}{2 (1)}$

Multiply $- 4 \cdot 1 \cdot - 8$ .

Multiply $- 4$ by $1$ .

$x = \frac{2 - \sqrt{4 - 4 \cdot - 8}}{2 (1)}$

Multiply $- 4$ by $- 8$ .

$x = \frac{2 - \sqrt{4 + 32}}{2 (1)}$

Add $4$ and $32$ .

$x = \frac{2 - \sqrt{36}}{2 (1)}$

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

$x = \frac{2 - \sqrt{6^{2}}}{2 (1)}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{2 - 1 \cdot 6}{2 (1)}$

Multiply $- 1$ by $6$ .

$x = \frac{2 - 6}{2 (1)}$

Subtract $6$ from $2$ .

$x = \frac{- 4}{2 (1)}$

Simplify the expression.

Multiply $2$ by $1$ .

$x = \frac{- 4}{2}$

Divide $- 4$ by $2$ .

$x = - 2$

Add $2$ to both sides of the equation.

$x + 2 = 0$

Step 3

Subtract $2$ from both sides of the equation.

$x = - 2$

Solve Using the Quadratic Formula x=(-(-2)+- square root of (-2)^2-4*1*-8)/(2(1))

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Solve Using the Quadratic Formula x=(-(-2)+- square root of (-2)^2-41-8)/(2(1))