Basic Math Examples

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

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Multiply

- 1

$- 1$ by

40

$40$ .

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

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

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)}

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

Step 1.3

Multiply

- 4 \cdot 1 \cdot - 400

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

Tap for more steps...

Step 1.3.1

Multiply

- 4

$- 4$ by

1

$1$ .

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

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

Step 1.3.2

Multiply

- 4

$- 4$ by

- 400

$- 400$ .

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

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

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

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

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

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

Step 2

Simplify with factoring out.

Tap for more steps...

Step 2.1

Multiply

2

$2$ by

1

$1$ .

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

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

Step 2.2

Factor

- 1

$- 1$ out of

- 40 \pm 40

$- 40 \pm 40$ .

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

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

Step 2.3

Rewrite

1600

$1600$ as

- 1 (- 1600)

$- 1 (- 1600)$ .

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

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

Step 2.4

Factor

- 1

$- 1$ out of

- 1 (- (- 40 \pm 40)) - 1 (- 1600)

$- 1 (- (- 40 \pm 40)) - 1 (- 1600)$ .

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

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

Step 2.5

Move the negative in front of the fraction.

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

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

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

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

Step 3

Use the positive value of the

\pm

$\pm$ to find the first solution.

Tap for more steps...

Step 3.1

Cancel the common factor of

- (- 40 + 40) - 1600

$- (- 40 + 40) - 1600$ and

2

$2$ .

Tap for more steps...

Step 3.1.1

Rewrite

- 1600

$- 1600$ as

- 1 (1600)

$- 1 (1600)$ .

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

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

Step 3.1.2

Factor

- 1

$- 1$ out of

- (- 40 + 40) - 1 (1600)

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

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

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

Step 3.1.3

Rewrite

- (- 40 + 40 + 1600)

$- (- 40 + 40 + 1600)$ as

- 1 (- 40 + 40 + 1600)

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

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

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

Step 3.1.4

Factor

2

$2$ out of

- 1 (- 40 + 40 + 1600)

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

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

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

Step 3.1.5

Cancel the common factors.

Tap for more steps...

Step 3.1.5.1

Factor

2

$2$ out of

2

$2$ .

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

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

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.

Tap for more steps...

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

$- (- 1 \cdot 800)$ .

Tap for more steps...

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.

Tap for more steps...

Step 4.1

Cancel the common factor of

$- (- 40 - 40) - 1600$ and

$2$ .

Tap for more steps...

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.

Tap for more steps...

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.

Tap for more steps...

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

$- (- 1 \cdot 760)$ .

Tap for more steps...

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.

$800, 760$