Finite Math Examples

$2 x^{2} + x + 15$

Step 1

Set $2 x^{2} + x + 15$ equal to $0$ .

$2 x^{2} + x + 15 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 2$ , $b = 1$ , and $c = 15$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (2 \cdot 15)}}{2 \cdot 2}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 2 \cdot 15}}{2 \cdot 2}$

Step 4.1.2

Multiply $- 4 \cdot 2 \cdot 15$ .

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Step 4.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{- 1 \pm \sqrt{1 - 8 \cdot 15}}{2 \cdot 2}$

Step 4.1.2.2

Multiply $- 8$ by $15$ .

$x = \frac{- 1 \pm \sqrt{1 - 120}}{2 \cdot 2}$

Step 4.1.3

Subtract $120$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 119}}{2 \cdot 2}$

Step 4.1.4

Rewrite $- 119$ as $- 1 (119)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 119}}{2 \cdot 2}$

Step 4.1.5

Rewrite $\sqrt{- 1 (119)}$ as $\sqrt{- 1} \cdot \sqrt{119}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{119}}{2 \cdot 2}$

Step 4.1.6

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

$x = \frac{- 1 \pm i \sqrt{119}}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$x = \frac{- 1 \pm i \sqrt{119}}{4}$