Calculus Examples

$x = \frac{- (- 8) + \sqrt{{(8)}^{2} - 4 \cdot 1 \cdot 9}}{2 (1)}$

Step 1

Remove parentheses.

$x = \frac{- (- 8) + \sqrt{8^{2} - 4 \cdot 1 \cdot 9}}{2 (1)}$

Step 2

Simplify $\frac{- (- 8) + \sqrt{8^{2} - 4 \cdot 1 \cdot 9}}{2 (1)}$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $- 1$ by $- 8$ .

$x = \frac{8 + \sqrt{8^{2} - 4 \cdot 1 \cdot 9}}{2 (1)}$

Step 2.1.2

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

$x = \frac{8 + \sqrt{64 - 4 \cdot 1 \cdot 9}}{2 (1)}$

Step 2.1.3

Multiply $- 4 \cdot 1 \cdot 9$ .

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Step 2.1.3.1

Multiply $- 4$ by $1$ .

$x = \frac{8 + \sqrt{64 - 4 \cdot 9}}{2 (1)}$

Step 2.1.3.2

Multiply $- 4$ by $9$ .

$x = \frac{8 + \sqrt{64 - 36}}{2 (1)}$

Step 2.1.4

Subtract $36$ from $64$ .

$x = \frac{8 + \sqrt{28}}{2 (1)}$

Step 2.1.5

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 2.1.5.1

Factor $4$ out of $28$ .

$x = \frac{8 + \sqrt{4 (7)}}{2 (1)}$

Step 2.1.5.2

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

$x = \frac{8 + \sqrt{2^{2} \cdot 7}}{2 (1)}$

Step 2.1.6

Pull terms out from under the radical.

$x = \frac{8 + 2 \sqrt{7}}{2 (1)}$

Step 2.2

Reduce the expression by cancelling the common factors.

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Step 2.2.1

Multiply $2$ by $1$ .

$x = \frac{8 + 2 \sqrt{7}}{2}$

Step 2.2.2

Cancel the common factor of $8 + 2 \sqrt{7}$ and $2$ .

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Step 2.2.2.1

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 4 + 2 \sqrt{7}}{2}$

Step 2.2.2.2

Factor $2$ out of $2 \sqrt{7}$ .

$x = \frac{2 \cdot 4 + 2 (\sqrt{7})}{2}$

Step 2.2.2.3

Factor $2$ out of $2 (4) + 2 (\sqrt{7})$ .

$x = \frac{2 (4 + \sqrt{7})}{2}$

Step 2.2.2.4

Cancel the common factors.

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Step 2.2.2.4.1

Factor $2$ out of $2$ .

$x = \frac{2 (4 + \sqrt{7})}{2 (1)}$

Step 2.2.2.4.2

Cancel the common factor.

$x = \frac{2 (4 + \sqrt{7})}{2 \cdot 1}$

Step 2.2.2.4.3

Rewrite the expression.

$x = \frac{4 + \sqrt{7}}{1}$

Step 2.2.2.4.4

Divide $4 + \sqrt{7}$ by $1$ .

$x = 4 + \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 4 + \sqrt{7}$

Decimal Form:

$x = 6.64575131 \dots$