Solve Using the Quadratic Formula x=(-3+- square root of 3^2-4124)/(2(1))

$x = \frac{- 3 + - \sqrt{3^{2} - 4 \cdot 1 \cdot 24}}{2 (1)}$

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 $1 \cdot - 1 = - 1$

$x = \frac{- 3 - \sqrt{3^{2} - 4 \cdot 1 \cdot 24}}{2 (1)}$

Step 2

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

Simplify the right side.

Simplify $\frac{- 3 - \sqrt{3^{2} - 4 \cdot 1 \cdot 24}}{2 (1)}$ .

Simplify the numerator.

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

$x = \frac{- 3 - \sqrt{9 - 4 \cdot 1 \cdot 24}}{2 (1)}$

Multiply $- 4 \cdot 1 \cdot 24$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 3 - \sqrt{9 - 4 \cdot 24}}{2 (1)}$

Multiply $- 4$ by $24$ .

$x = \frac{- 3 - \sqrt{9 - 96}}{2 (1)}$

Subtract $96$ from $9$ .

$x = \frac{- 3 - \sqrt{- 87}}{2 (1)}$

Rewrite $- 87$ as $- 1 (87)$ .

$x = \frac{- 3 - \sqrt{- 1 (87)}}{2 (1)}$

Rewrite $\sqrt{- 1 (87)}$ as $\sqrt{- 1} \cdot \sqrt{87}$ .

$x = \frac{- 3 - (\sqrt{- 1} \cdot \sqrt{87})}{2 (1)}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 3 - i \sqrt{87}}{2 (1)}$

Simplify with factoring out.

Multiply $2$ by $1$ .

$x = \frac{- 3 - i \sqrt{87}}{2}$

Rewrite $- 3$ as $- 1 (3)$ .

$x = \frac{- 1 (3) - i \sqrt{87}}{2}$

Factor $- 1$ out of $- i \sqrt{87}$ .

$x = \frac{- 1 (3) - (i \sqrt{87})}{2}$

Factor $- 1$ out of $- 1 (3) - (i \sqrt{87})$ .

$x = \frac{- 1 (3 + i \sqrt{87})}{2}$

Move the negative in front of the fraction.

$x = - \frac{3 + i \sqrt{87}}{2}$

Add $\frac{3 + i \sqrt{87}}{2}$ to both sides of the equation.

$x + \frac{3 + i \sqrt{87}}{2} = 0$

Step 3

Simplify $x + \frac{3 + i \sqrt{87}}{2}$ .

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x \cdot \frac{2}{2} + \frac{3 + i \sqrt{87}}{2} = 0$

Simplify terms.

Combine $x$ and $\frac{2}{2}$ .

$\frac{x \cdot 2}{2} + \frac{3 + i \sqrt{87}}{2} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 + i \sqrt{87}}{2} = 0$

Simplify the numerator.

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 3 + i \sqrt{87}}{2} = 0$

Reorder terms.

$\frac{i \sqrt{87} + 2 x + 3}{2} = 0$

Step 4

Set the numerator equal to zero.

$i \sqrt{87} + 2 x + 3 = 0$

Step 5

Solve the equation for $x$ .

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

Subtract $i \sqrt{87}$ from both sides of the equation.

$2 x + 3 = - i \sqrt{87}$

Subtract $3$ from both sides of the equation.

$2 x = - i \sqrt{87} - 3$

Reorder $- i \sqrt{87}$ and $- 3$ .

$2 x = - 3 - i \sqrt{87}$

Divide each term in $2 x = - 3 - i \sqrt{87}$ by $2$ and simplify.

Divide each term in $2 x = - 3 - i \sqrt{87}$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2} + \frac{- i \sqrt{87}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2} + \frac{- i \sqrt{87}}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2} + \frac{- i \sqrt{87}}{2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{3}{2} + \frac{- i \sqrt{87}}{2}$

Move the negative in front of the fraction.

$x = - \frac{3}{2} - \frac{i \sqrt{87}}{2}$

Solve Using the Quadratic Formula x=(-3+- square root of 3^2-4*1*24)/(2(1))

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Solve Using the Quadratic Formula x=(-3+- square root of 3^2-4124)/(2(1))