Algebra Examples

$2 x^{2} + x + 6 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 2$ , $b = 1$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (2 \cdot 6)}}{2 \cdot 2}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}$

Step 3.1.2

Multiply $- 4 \cdot 2 \cdot 6$ .

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Step 3.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{- 1 \pm \sqrt{1 - 8 \cdot 6}}{2 \cdot 2}$

Step 3.1.2.2

Multiply $- 8$ by $6$ .

$x = \frac{- 1 \pm \sqrt{1 - 48}}{2 \cdot 2}$

Step 3.1.3

Subtract $48$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 47}}{2 \cdot 2}$

Step 3.1.4

Rewrite $- 47$ as $- 1 (47)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 47}}{2 \cdot 2}$

Step 3.1.5

Rewrite $\sqrt{- 1 (47)}$ as $\sqrt{- 1} \cdot \sqrt{47}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{47}}{2 \cdot 2}$

Step 3.1.6

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

$x = \frac{- 1 \pm i \sqrt{47}}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

$x = \frac{- 1 \pm i \sqrt{47}}{4}$