Solve Using the Quadratic Formula x^2-8x+30=0

$x^{2} - 8 x + 30 = 0$

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 $a = 1$ , $b = - 8$ , and $c = 30$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 30)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 30}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 30$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 30}}{2 \cdot 1}$

Multiply $- 4$ by $30$ .

$x = \frac{8 \pm \sqrt{64 - 120}}{2 \cdot 1}$

Subtract $120$ from $64$ .

$x = \frac{8 \pm \sqrt{- 56}}{2 \cdot 1}$

Rewrite $- 56$ as $- 1 (56)$ .

$x = \frac{8 \pm \sqrt{- 1 \cdot 56}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (56)}$ as $\sqrt{- 1} \cdot \sqrt{56}$ .

$x = \frac{8 \pm \sqrt{- 1} \cdot \sqrt{56}}{2 \cdot 1}$

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

$x = \frac{8 \pm i \cdot \sqrt{56}}{2 \cdot 1}$

Rewrite $56$ as $2^{2} \cdot 14$ .

Factor $4$ out of $56$ .

$x = \frac{8 \pm i \cdot \sqrt{4 (14)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{8 \pm i \cdot \sqrt{2^{2} \cdot 14}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm i \cdot (2 \sqrt{14})}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{8 \pm 2 i \sqrt{14}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 i \sqrt{14}}{2}$

Simplify $\frac{8 \pm 2 i \sqrt{14}}{2}$ .

$x = 4 \pm i \sqrt{14}$