Algebra Examples

$\frac{- 3 + - \sqrt{{(3)}^{2} + 4 (10) (2)}}{2 (10)}$

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 $1 \cdot - 1 = - 1$

$\frac{- 3 - \sqrt{{(3)}^{2} + 4 (10) (2)}}{2 (10)}$

Step 2

Set $\frac{- 3 + - \sqrt{{(3)}^{2} + 4 (10) (2)}}{2 (10)}$ equal to $0$ .

$\frac{- 3 + - \sqrt{{(3)}^{2} + 4 (10) (2)}}{2 (10)} = 0$

Step 3

Simplify the left side.

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Step 3.1

Simplify $\frac{- 3 + - \sqrt{{(3)}^{2} + 4 (10) (2)}}{2 (10)}$ .

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Step 3.1.1

Simplify the numerator.

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Step 3.1.1.1

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

$\frac{- 3 - \sqrt{9 + 4 (10) \cdot 2}}{2 (10)} = 0$

Step 3.1.1.2

Multiply $4 (10) \cdot 2$ .

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Step 3.1.1.2.1

Multiply $4$ by $10$ .

$\frac{- 3 - \sqrt{9 + 40 \cdot 2}}{2 (10)} = 0$

Step 3.1.1.2.2

Multiply $40$ by $2$ .

$\frac{- 3 - \sqrt{9 + 80}}{2 (10)} = 0$

Step 3.1.1.3

Add $9$ and $80$ .

$\frac{- 3 - \sqrt{89}}{2 (10)} = 0$

Step 3.1.2

Simplify with factoring out.

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Step 3.1.2.1

Multiply $2$ by $10$ .

$\frac{- 3 - \sqrt{89}}{20} = 0$

Step 3.1.2.2

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

$\frac{- 1 (3) - \sqrt{89}}{20} = 0$

Step 3.1.2.3

Factor $- 1$ out of $- \sqrt{89}$ .

$\frac{- 1 (3) - (\sqrt{89})}{20} = 0$

Step 3.1.2.4

Factor $- 1$ out of $- 1 (3) - (\sqrt{89})$ .

$\frac{- 1 (3 + \sqrt{89})}{20} = 0$

Step 3.1.2.5

Move the negative in front of the fraction.

$- \frac{3 + \sqrt{89}}{20} = 0$

Step 4

Set the numerator equal to zero.

$3 + \sqrt{89} = 0$

Step 5

Since $3 + \sqrt{89} \neq 0$ , there are no solutions.

No solution