Algebra Examples

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

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.

Tap for more steps...

Step 2.1

Simplify the right side.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Simplify the numerator.

Tap for more steps...

Step 2.1.1.1.1

Multiply $- 1$ by $- 2$ .

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

Step 2.1.1.1.2

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

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

Step 2.1.1.1.3

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

Tap for more steps...

Step 2.1.1.1.3.1

Multiply $- 4$ by $1$ .

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

Step 2.1.1.1.3.2

Multiply $- 4$ by $- 8$ .

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

Step 2.1.1.1.4

Add $4$ and $32$ .

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

Step 2.1.1.1.5

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

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

Step 2.1.1.1.6

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

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

Step 2.1.1.1.7

Multiply $- 1$ by $6$ .

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

Step 2.1.1.1.8

Subtract $6$ from $2$ .

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

Step 2.1.1.2

Simplify the expression.

Tap for more steps...

Step 2.1.1.2.1

Multiply $2$ by $1$ .

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

Step 2.1.1.2.2

Divide $- 4$ by $2$ .

$x = - 2$

Step 2.2

Add $2$ to both sides of the equation.

$x + 2 = 0$

Step 3

Subtract $2$ from both sides of the equation.

$x = - 2$