Algebra Examples

x = \frac{3 + - \sqrt{{(- 3)}^{2} - 4 \cdot 2 \cdot - 5}}{2 (2)}

$x = \frac{3 + - \sqrt{{(- 3)}^{2} - 4 \cdot 2 \cdot - 5}}{2 (2)}$

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

$1 \cdot - 1 = - 1$

x = \frac{3 - \sqrt{{(- 3)}^{2} - 4 \cdot 2 \cdot - 5}}{2 (2)}

$x = \frac{3 - \sqrt{{(- 3)}^{2} - 4 \cdot 2 \cdot - 5}}{2 (2)}$

Step 2

Move all terms to the left side of the equation and simplify.

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Step 2.1

Simplify the right side.

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Step 2.1.1

Simplify

\frac{3 - \sqrt{{(- 3)}^{2} - 4 \cdot 2 \cdot - 5}}{2 (2)}

$\frac{3 - \sqrt{{(- 3)}^{2} - 4 \cdot 2 \cdot - 5}}{2 (2)}$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Raise

- 3

$- 3$ to the power of

2

$2$ .

x = \frac{3 - \sqrt{9 - 4 \cdot 2 \cdot - 5}}{2 (2)}

$x = \frac{3 - \sqrt{9 - 4 \cdot 2 \cdot - 5}}{2 (2)}$

Step 2.1.1.1.2

Multiply

- 4 \cdot 2 \cdot - 5

$- 4 \cdot 2 \cdot - 5$ .

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Step 2.1.1.1.2.1

Multiply

- 4

$- 4$ by

2

$2$ .

x = \frac{3 - \sqrt{9 - 8 \cdot - 5}}{2 (2)}

$x = \frac{3 - \sqrt{9 - 8 \cdot - 5}}{2 (2)}$

Step 2.1.1.1.2.2

Multiply

- 8

$- 8$ by

- 5

$- 5$ .

x = \frac{3 - \sqrt{9 + 40}}{2 (2)}

$x = \frac{3 - \sqrt{9 + 40}}{2 (2)}$

x = \frac{3 - \sqrt{9 + 40}}{2 (2)}

$x = \frac{3 - \sqrt{9 + 40}}{2 (2)}$

Step 2.1.1.1.3

Add

9

$9$ and

40

$40$ .

x = \frac{3 - \sqrt{49}}{2 (2)}

$x = \frac{3 - \sqrt{49}}{2 (2)}$

Step 2.1.1.1.4

Rewrite

49

$49$ as

7^{2}

$7^{2}$ .

x = \frac{3 - \sqrt{7^{2}}}{2 (2)}

$x = \frac{3 - \sqrt{7^{2}}}{2 (2)}$

Step 2.1.1.1.5

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

x = \frac{3 - 1 \cdot 7}{2 (2)}

$x = \frac{3 - 1 \cdot 7}{2 (2)}$

Step 2.1.1.1.6

Multiply

- 1

$- 1$ by

7

$7$ .

x = \frac{3 - 7}{2 (2)}

$x = \frac{3 - 7}{2 (2)}$

Step 2.1.1.1.7

Subtract

7

$7$ from

3

$3$ .

x = \frac{- 4}{2 (2)}

$x = \frac{- 4}{2 (2)}$

x = \frac{- 4}{2 (2)}

$x = \frac{- 4}{2 (2)}$

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

Multiply

2

$2$ by

2

$2$ .

x = \frac{- 4}{4}

$x = \frac{- 4}{4}$

Step 2.1.1.2.2

Divide

- 4

$- 4$ by

4

$4$ .

x = - 1

$x = - 1$

x = - 1

$x = - 1$

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 2.2

Add

1

$1$ to both sides of the equation.

x + 1 = 0

$x + 1 = 0$

x + 1 = 0

$x + 1 = 0$

Step 3

Subtract

1

$1$ from both sides of the equation.

x = - 1

$x = - 1$