Algebra Examples

$x = \frac{- (- 4) + - \sqrt{{(- 4)}^{2} - 4 \cdot 1 \cdot 1}}{2 (1)}$

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 $1 \cdot - 1 = - 1$

$x = \frac{- (- 4) - \sqrt{{(- 4)}^{2} - 4 \cdot 1 \cdot 1}}{2 (1)}$

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 $\frac{- (- 4) - \sqrt{{(- 4)}^{2} - 4 \cdot 1 \cdot 1}}{2 (1)}$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Multiply $- 1$ by $- 4$ .

$x = \frac{4 - \sqrt{{(- 4)}^{2} - 4 \cdot 1 \cdot 1}}{2 (1)}$

Step 2.1.1.1.2

Raise $- 4$ to the power of $2$ .

$x = \frac{4 - \sqrt{16 - 4 \cdot 1 \cdot 1}}{2 (1)}$

Step 2.1.1.1.3

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

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Step 2.1.1.1.3.1

Multiply $- 4$ by $1$ .

$x = \frac{4 - \sqrt{16 - 4 \cdot 1}}{2 (1)}$

Step 2.1.1.1.3.2

Multiply $- 4$ by $1$ .

$x = \frac{4 - \sqrt{16 - 4}}{2 (1)}$

Step 2.1.1.1.4

Subtract $4$ from $16$ .

$x = \frac{4 - \sqrt{12}}{2 (1)}$

Step 2.1.1.1.5

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.1.1.1.5.1

Factor $4$ out of $12$ .

$x = \frac{4 - \sqrt{4 (3)}}{2 (1)}$

Step 2.1.1.1.5.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{4 - \sqrt{2^{2} \cdot 3}}{2 (1)}$

Step 2.1.1.1.6

Pull terms out from under the radical.

$x = \frac{4 - (2 \sqrt{3})}{2 (1)}$

Step 2.1.1.1.7

Multiply $2$ by $- 1$ .

$x = \frac{4 - 2 \sqrt{3}}{2 (1)}$

Step 2.1.1.2

Reduce the expression by cancelling the common factors.

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Step 2.1.1.2.1

Multiply $2$ by $1$ .

$x = \frac{4 - 2 \sqrt{3}}{2}$

Step 2.1.1.2.2

Cancel the common factor of $4 - 2 \sqrt{3}$ and $2$ .

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Step 2.1.1.2.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 2 - 2 \sqrt{3}}{2}$

Step 2.1.1.2.2.2

Factor $2$ out of $- 2 \sqrt{3}$ .

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

Step 2.1.1.2.2.3

Factor $2$ out of $2 (2) + 2 (- \sqrt{3})$ .

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

Step 2.1.1.2.2.4

Cancel the common factors.

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Step 2.1.1.2.2.4.1

Factor $2$ out of $2$ .

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

Step 2.1.1.2.2.4.2

Cancel the common factor.

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

Step 2.1.1.2.2.4.3

Rewrite the expression.

$x = \frac{2 - \sqrt{3}}{1}$

Step 2.1.1.2.2.4.4

Divide $2 - \sqrt{3}$ by $1$ .

$x = 2 - \sqrt{3}$

Step 2.2

Move all the expressions to the left side of the equation.

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$x - 2 = - \sqrt{3}$

Step 2.2.2

Add $\sqrt{3}$ to both sides of the equation.

$x - 2 + \sqrt{3} = 0$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $2$ to both sides of the equation.

$x + \sqrt{3} = 2$

Step 3.2

Subtract $\sqrt{3}$ from both sides of the equation.

$x = 2 - \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 2 - \sqrt{3}$

Decimal Form:

$x = 0.26794919 \dots$