Basic Math Examples

$0 = a^{2} - 13 a + 57$

Step 1

Rewrite the equation as $a^{2} - 13 a + 57 = 0$ .

$a^{2} - 13 a + 57 = 0$

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 $a = 1$ , $b = - 13$ , and $c = 57$ into the quadratic formula and solve for $a$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (1 \cdot 57)}}{2 \cdot 1}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $- 13$ to the power of $2$ .

$a = \frac{13 \pm \sqrt{169 - 4 \cdot 1 \cdot 57}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 57$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $1$ .

$a = \frac{13 \pm \sqrt{169 - 4 \cdot 57}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $57$ .

$a = \frac{13 \pm \sqrt{169 - 228}}{2 \cdot 1}$

Step 4.1.3

Subtract $228$ from $169$ .

$a = \frac{13 \pm \sqrt{- 59}}{2 \cdot 1}$

Step 4.1.4

Rewrite $- 59$ as $- 1 (59)$ .

$a = \frac{13 \pm \sqrt{- 1 \cdot 59}}{2 \cdot 1}$

Step 4.1.5

Rewrite $\sqrt{- 1 (59)}$ as $\sqrt{- 1} \cdot \sqrt{59}$ .

$a = \frac{13 \pm \sqrt{- 1} \cdot \sqrt{59}}{2 \cdot 1}$

Step 4.1.6

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

$a = \frac{13 \pm i \sqrt{59}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$a = \frac{13 \pm i \sqrt{59}}{2}$

Step 5

The final answer is the combination of both solutions.

$a = \frac{13 + i \sqrt{59}}{2}, \frac{13 - i \sqrt{59}}{2}$