Solve Using the Quadratic Formula x=(-2+- square root of 2^2-41-4)/(2(1))

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

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 $1 \cdot - 1 = - 1$

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

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

Simplify the right side.

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

Simplify the numerator.

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 4$ .

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

Add $4$ and $16$ .

$x = \frac{- 2 - \sqrt{20}}{2 (1)}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \frac{- 2 - \sqrt{4 (5)}}{2 (1)}$

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

$x = \frac{- 2 - \sqrt{2^{2} \cdot 5}}{2 (1)}$

Pull terms out from under the radical.

$x = \frac{- 2 - (2 \sqrt{5})}{2 (1)}$

Multiply $2$ by $- 1$ .

$x = \frac{- 2 - 2 \sqrt{5}}{2 (1)}$

Reduce the expression by cancelling the common factors.

Multiply $2$ by $1$ .

$x = \frac{- 2 - 2 \sqrt{5}}{2}$

Cancel the common factor of $- 2 - 2 \sqrt{5}$ and $2$ .

Factor $2$ out of $- 2$ .

$x = \frac{2 \cdot - 1 - 2 \sqrt{5}}{2}$

Factor $2$ out of $- 2 \sqrt{5}$ .

$x = \frac{2 \cdot - 1 + 2 (- \sqrt{5})}{2}$

Factor $2$ out of $2 (- 1) + 2 (- \sqrt{5})$ .

$x = \frac{2 (- 1 - \sqrt{5})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (- 1 - \sqrt{5})}{2 (1)}$

Cancel the common factor.

$x = \frac{2 (- 1 - \sqrt{5})}{2 \cdot 1}$

Rewrite the expression.

$x = \frac{- 1 - \sqrt{5}}{1}$

Divide $- 1 - \sqrt{5}$ by $1$ .

$x = - 1 - \sqrt{5}$

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

Add $1$ to both sides of the equation.

$x + 1 = - \sqrt{5}$

Add $\sqrt{5}$ to both sides of the equation.

$x + 1 + \sqrt{5} = 0$

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

Subtract $1$ from both sides of the equation.

$x + \sqrt{5} = - 1$

Subtract $\sqrt{5}$ from both sides of the equation.

$x = - 1 - \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$x = - 1 - \sqrt{5}$

Decimal Form:

$x = - 3.23606797 \dots$

Solve Using the Quadratic Formula x=(-2+- square root of 2^2-4*1*-4)/(2(1))

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Solve Using the Quadratic Formula x=(-2+- square root of 2^2-41-4)/(2(1))