Algebra Examples

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

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 $1 \cdot - 1 = - 1$

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

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $- 8$ .

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

Step 2.2

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

$\frac{8 - \sqrt{64 - 4 \cdot 2 \cdot - 1}}{2 (2)}$

Step 2.3

Multiply $- 4 \cdot 2 \cdot - 1$ .

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Step 2.3.1

Multiply $- 4$ by $2$ .

$\frac{8 - \sqrt{64 - 8 \cdot - 1}}{2 (2)}$

Step 2.3.2

Multiply $- 8$ by $- 1$ .

$\frac{8 - \sqrt{64 + 8}}{2 (2)}$

Step 2.4

Add $64$ and $8$ .

$\frac{8 - \sqrt{72}}{2 (2)}$

Step 2.5

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 2.5.1

Factor $36$ out of $72$ .

$\frac{8 - \sqrt{36 (2)}}{2 (2)}$

Step 2.5.2

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

$\frac{8 - \sqrt{6^{2} \cdot 2}}{2 (2)}$

Step 2.6

Pull terms out from under the radical.

$\frac{8 - (6 \sqrt{2})}{2 (2)}$

Step 2.7

Multiply $6$ by $- 1$ .

$\frac{8 - 6 \sqrt{2}}{2 (2)}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $2$ by $2$ .

$\frac{8 - 6 \sqrt{2}}{4}$

Step 3.2

Cancel the common factor of $8 - 6 \sqrt{2}$ and $4$ .

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Step 3.2.1

Factor $2$ out of $8$ .

$\frac{2 (4) - 6 \sqrt{2}}{4}$

Step 3.2.2

Factor $2$ out of $- 6 \sqrt{2}$ .

$\frac{2 (4) + 2 (- 3 \sqrt{2})}{4}$

Step 3.2.3

Factor $2$ out of $2 (4) + 2 (- 3 \sqrt{2})$ .

$\frac{2 (4 - 3 \sqrt{2})}{4}$

Step 3.2.4

Cancel the common factors.

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Step 3.2.4.1

Factor $2$ out of $4$ .

$\frac{2 (4 - 3 \sqrt{2})}{2 \cdot 2}$

Step 3.2.4.2

Cancel the common factor.

$\frac{2 (4 - 3 \sqrt{2})}{2 \cdot 2}$

Step 3.2.4.3

Rewrite the expression.

$\frac{4 - 3 \sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4 - 3 \sqrt{2}}{2}$

Decimal Form:

$- 0.12132034 \dots$