Basic Math Examples

$\frac{- (40) \pm \sqrt{{(40)}^{2}} - 4 \cdot 1 \cdot - 400}{2 (1)}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $40$ .

$\frac{- 40 \pm \sqrt{40^{2}} - 4 \cdot 1 \cdot - 400}{2 (1)}$

Step 1.2

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

$\frac{- 40 \pm 40 - 4 \cdot 1 \cdot - 400}{2 (1)}$

Step 1.3

Multiply $- 4 \cdot 1 \cdot - 400$ .

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Step 1.3.1

Multiply $- 4$ by $1$ .

$\frac{- 40 \pm 40 - 4 \cdot - 400}{2 (1)}$

Step 1.3.2

Multiply $- 4$ by $- 400$ .

$\frac{- 40 \pm 40 + 1600}{2 (1)}$

Step 2

Simplify with factoring out.

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Step 2.1

Multiply $2$ by $1$ .

$\frac{- 40 \pm 40 + 1600}{2}$

Step 2.2

Factor $- 1$ out of $- 40 \pm 40$ .

$\frac{- 1 (- (- 40 \pm 40)) + 1600}{2}$

Step 2.3

Rewrite $1600$ as $- 1 (- 1600)$ .

$\frac{- 1 (- (- 40 \pm 40)) - 1 (- 1600)}{2}$

Step 2.4

Factor $- 1$ out of $- 1 (- (- 40 \pm 40)) - 1 (- 1600)$ .

$\frac{- 1 (- (- 40 \pm 40) - 1600)}{2}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{- (- 40 \pm 40) - 1600}{2}$

Step 3

Use the positive value of the $\pm$ to find the first solution.

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Step 3.1

Cancel the common factor of $- (- 40 + 40) - 1600$ and $2$ .

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Step 3.1.1

Rewrite $- 1600$ as $- 1 (1600)$ .

$- \frac{- (- 40 + 40) - 1 (1600)}{2}$

Step 3.1.2

Factor $- 1$ out of $- (- 40 + 40) - 1 (1600)$ .

$- \frac{- (- 40 + 40 + 1600)}{2}$

Step 3.1.3

Rewrite $- (- 40 + 40 + 1600)$ as $- 1 (- 40 + 40 + 1600)$ .

$- \frac{- 1 (- 40 + 40 + 1600)}{2}$

Step 3.1.4

Factor $2$ out of $- 1 (- 40 + 40 + 1600)$ .

$- \frac{2 (- 1 (- 20 + 20 + 800))}{2}$

Step 3.1.5

Cancel the common factors.

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Step 3.1.5.1

Factor $2$ out of $2$ .

$- \frac{2 (- 1 (- 20 + 20 + 800))}{2 (1)}$

Step 3.1.5.2

Cancel the common factor.

$- \frac{2 (- 1 (- 20 + 20 + 800))}{2 \cdot 1}$

Step 3.1.5.3

Rewrite the expression.

$- \frac{- 1 (- 20 + 20 + 800)}{1}$

Step 3.1.5.4

Divide $- 1 (- 20 + 20 + 800)$ by $1$ .

$- (- 1 (- 20 + 20 + 800))$

Step 3.2

Simplify the expression.

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Step 3.2.1

Rewrite $- 1 (- 20 + 20 + 800)$ as $- (- 20 + 20 + 800)$ .

$- - (- 20 + 20 + 800)$

Step 3.2.2

Add $- 20$ and $20$ .

$- - (0 + 800)$

Step 3.2.3

Add $0$ and $800$ .

$- (- 1 \cdot 800)$

Step 3.3

Multiply $- (- 1 \cdot 800)$ .

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Step 3.3.1

Multiply $- 1$ by $800$ .

$- - 800$

Step 3.3.2

Multiply $- 1$ by $- 800$ .

$800$

Step 4

Use the negative value of the $\pm$ to find the second solution.

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Step 4.1

Cancel the common factor of $- (- 40 - 40) - 1600$ and $2$ .

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Step 4.1.1

Rewrite $- 1600$ as $- 1 (1600)$ .

$- \frac{- (- 40 - 40) - 1 (1600)}{2}$

Step 4.1.2

Factor $- 1$ out of $- (- 40 - 40) - 1 (1600)$ .

$- \frac{- (- 40 - 40 + 1600)}{2}$

Step 4.1.3

Rewrite $- (- 40 - 40 + 1600)$ as $- 1 (- 40 - 40 + 1600)$ .

$- \frac{- 1 (- 40 - 40 + 1600)}{2}$

Step 4.1.4

Factor $2$ out of $- 1 (- 40 - 40 + 1600)$ .

$- \frac{2 (- 1 (- 20 - 20 + 800))}{2}$

Step 4.1.5

Cancel the common factors.

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Step 4.1.5.1

Factor $2$ out of $2$ .

$- \frac{2 (- 1 (- 20 - 20 + 800))}{2 (1)}$

Step 4.1.5.2

Cancel the common factor.

$- \frac{2 (- 1 (- 20 - 20 + 800))}{2 \cdot 1}$

Step 4.1.5.3

Rewrite the expression.

$- \frac{- 1 (- 20 - 20 + 800)}{1}$

Step 4.1.5.4

Divide $- 1 (- 20 - 20 + 800)$ by $1$ .

$- (- 1 (- 20 - 20 + 800))$

Step 4.2

Simplify the expression.

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Step 4.2.1

Rewrite $- 1 (- 20 - 20 + 800)$ as $- (- 20 - 20 + 800)$ .

$- - (- 20 - 20 + 800)$

Step 4.2.2

Subtract $20$ from $- 20$ .

$- - (- 40 + 800)$

Step 4.2.3

Add $- 40$ and $800$ .

$- (- 1 \cdot 760)$

Step 4.3

Multiply $- (- 1 \cdot 760)$ .

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Step 4.3.1

Multiply $- 1$ by $760$ .

$- - 760$

Step 4.3.2

Multiply $- 1$ by $- 760$ .

$760$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

$800, 760$