Solve Using the Quadratic Formula x^2+10x+7=0

$x^{2} + 10 x + 7 = 0$

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 $a = 1$ , $b = 10$ , and $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot 7}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 7$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 7}}{2 \cdot 1}$

Multiply $- 4$ by $7$ .

$x = \frac{- 10 \pm \sqrt{100 - 28}}{2 \cdot 1}$

Subtract $28$ from $100$ .

$x = \frac{- 10 \pm \sqrt{72}}{2 \cdot 1}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$x = \frac{- 10 \pm \sqrt{36 (2)}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 10 \pm \sqrt{6^{2} \cdot 2}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 10 \pm 6 \sqrt{2}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 6 \sqrt{2}}{2}$

Simplify $\frac{- 10 \pm 6 \sqrt{2}}{2}$ .

$x = - 5 \pm 3 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 5 \pm 3 \sqrt{2}$

Decimal Form:

$x = - 0.75735931 \dots, - 9.24264068 \dots$