Solve Using the Quadratic Formula x^2-7x-2=0

$x^{2} - 7 x - 2 = 0$

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 $a = 1$ , $b = - 7$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (1 \cdot - 2)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 1 \cdot - 2}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 2$ .

Multiply $- 4$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot - 2}}{2 \cdot 1}$

Multiply $- 4$ by $- 2$ .

$x = \frac{7 \pm \sqrt{49 + 8}}{2 \cdot 1}$

Add $49$ and $8$ .

$x = \frac{7 \pm \sqrt{57}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{57}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{57}}{2}$

Decimal Form:

$x = 7.27491721 \dots, - 0.27491721 \dots$