Precalculus Examples

$3 x^{2} + x + 12 = 0$

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 $a = 3$ , $b = 1$ , and $c = 12$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (3 \cdot 12)}}{2 \cdot 3}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 3 \cdot 12}}{2 \cdot 3}$

Step 3.1.2

Multiply $- 4 \cdot 3 \cdot 12$ .

Tap for more steps...

Step 3.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{- 1 \pm \sqrt{1 - 12 \cdot 12}}{2 \cdot 3}$

Step 3.1.2.2

Multiply $- 12$ by $12$ .

$x = \frac{- 1 \pm \sqrt{1 - 144}}{2 \cdot 3}$

Step 3.1.3

Subtract $144$ from $1$ .

$x = \frac{- 1 \pm \sqrt{- 143}}{2 \cdot 3}$

Step 3.1.4

Rewrite $- 143$ as $- 1 (143)$ .

$x = \frac{- 1 \pm \sqrt{- 1 \cdot 143}}{2 \cdot 3}$

Step 3.1.5

Rewrite $\sqrt{- 1 (143)}$ as $\sqrt{- 1} \cdot \sqrt{143}$ .

$x = \frac{- 1 \pm \sqrt{- 1} \cdot \sqrt{143}}{2 \cdot 3}$

Step 3.1.6

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

$x = \frac{- 1 \pm i \sqrt{143}}{2 \cdot 3}$

Step 3.2

Multiply $2$ by $3$ .

$x = \frac{- 1 \pm i \sqrt{143}}{6}$