Pre-Algebra Examples

$\frac{- 3 + \sqrt{3^{2} - 4 \cdot 1 \cdot 18}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $3$ to the power of $2$ .

$\frac{- 3 + \sqrt{9 - 4 \cdot 1 \cdot 18}}{2}$

Step 1.2

Multiply $- 4 \cdot 1 \cdot 18$ .

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Step 1.2.1

Multiply $- 4$ by $1$ .

$\frac{- 3 + \sqrt{9 - 4 \cdot 18}}{2}$

Step 1.2.2

Multiply $- 4$ by $18$ .

$\frac{- 3 + \sqrt{9 - 72}}{2}$

Step 1.3

Subtract $72$ from $9$ .

$\frac{- 3 + \sqrt{- 63}}{2}$

Step 1.4

Rewrite $- 63$ as $- 1 (63)$ .

$\frac{- 3 + \sqrt{- 1 (63)}}{2}$

Step 1.5

Rewrite $\sqrt{- 1 (63)}$ as $\sqrt{- 1} \cdot \sqrt{63}$ .

$\frac{- 3 + \sqrt{- 1} \cdot \sqrt{63}}{2}$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{- 3 + i \cdot \sqrt{63}}{2}$

Step 1.7

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 1.7.1

Factor $9$ out of $63$ .

$\frac{- 3 + i \cdot \sqrt{9 (7)}}{2}$

Step 1.7.2

Rewrite $9$ as $3^{2}$ .

$\frac{- 3 + i \cdot \sqrt{3^{2} \cdot 7}}{2}$

Step 1.8

Pull terms out from under the radical.

$\frac{- 3 + i \cdot (3 \sqrt{7})}{2}$

Step 1.9

Move $3$ to the left of $i$ .

$\frac{- 3 + 3 i \sqrt{7}}{2}$

Step 2

Simplify with factoring out.

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Step 2.1

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) + 3 i \sqrt{7}}{2}$

Step 2.2

Factor $- 1$ out of $3 i \sqrt{7}$ .

$\frac{- 1 (3) - (- 3 i \sqrt{7})}{2}$

Step 2.3

Factor $- 1$ out of $- 1 (3) - (- 3 i \sqrt{7})$ .

$\frac{- 1 (3 - 3 i \sqrt{7})}{2}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{3 - 3 i \sqrt{7}}{2}$