Solve Using the Quadratic Formula x^2-14x+34=0

$x^{2} - 14 x + 34 = 0$

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 $a = 1$ , $b = - 14$ , and $c = 34$ into the quadratic formula and solve for $x$ .

$\frac{14 \pm \sqrt{{(- 14)}^{2} - 4 \cdot (1 \cdot 34)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 14$ to the power of $2$ .

$x = \frac{14 \pm \sqrt{196 - 4 \cdot 1 \cdot 34}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 34$ .

Multiply $- 4$ by $1$ .

$x = \frac{14 \pm \sqrt{196 - 4 \cdot 34}}{2 \cdot 1}$

Multiply $- 4$ by $34$ .

$x = \frac{14 \pm \sqrt{196 - 136}}{2 \cdot 1}$

Subtract $136$ from $196$ .

$x = \frac{14 \pm \sqrt{60}}{2 \cdot 1}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$x = \frac{14 \pm \sqrt{4 (15)}}{2 \cdot 1}$

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

$x = \frac{14 \pm \sqrt{2^{2} \cdot 15}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{14 \pm 2 \sqrt{15}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{14 \pm 2 \sqrt{15}}{2}$

Simplify $\frac{14 \pm 2 \sqrt{15}}{2}$ .

$x = 7 \pm \sqrt{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 7 \pm \sqrt{15}$

Decimal Form:

$x = 10.87298334 \dots, 3.12701665 \dots$