Algebra Examples

$x^{2} + 5 x + 11$

Step 1

Set $x^{2} + 5 x + 11$ equal to $0$ .

$x^{2} + 5 x + 11 = 0$

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 $a = 1$ , $b = 5$ , and $c = 11$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (1 \cdot 11)}}{2 \cdot 1}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 1 \cdot 11}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 11$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 11}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $11$ .

$x = \frac{- 5 \pm \sqrt{25 - 44}}{2 \cdot 1}$

Step 4.1.3

Subtract $44$ from $25$ .

$x = \frac{- 5 \pm \sqrt{- 19}}{2 \cdot 1}$

Step 4.1.4

Rewrite $- 19$ as $- 1 (19)$ .

$x = \frac{- 5 \pm \sqrt{- 1 \cdot 19}}{2 \cdot 1}$

Step 4.1.5

Rewrite $\sqrt{- 1 (19)}$ as $\sqrt{- 1} \cdot \sqrt{19}$ .

$x = \frac{- 5 \pm \sqrt{- 1} \cdot \sqrt{19}}{2 \cdot 1}$

Step 4.1.6

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

$x = \frac{- 5 \pm i \sqrt{19}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 5 \pm i \sqrt{19}}{2}$