Algebra Examples

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

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 $1 \cdot - 1 = - 1$

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

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

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

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

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

Step 2.1.1.1.2

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

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Step 2.1.1.1.2.1

Multiply $- 4$ by $2$ .

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

Step 2.1.1.1.2.2

Multiply $- 8$ by $- 5$ .

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

Step 2.1.1.1.3

Add $9$ and $40$ .

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

Step 2.1.1.1.4

Rewrite $49$ as $7^{2}$ .

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

Step 2.1.1.1.5

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

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

Step 2.1.1.1.6

Multiply $- 1$ by $7$ .

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

Step 2.1.1.1.7

Subtract $7$ from $3$ .

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

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

Multiply $2$ by $2$ .

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

Step 2.1.1.2.2

Divide $- 4$ by $4$ .

$x = - 1$

Step 2.2

Add $1$ to both sides of the equation.

$x + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

$x = - 1$