Solve Using the Quadratic Formula x^2+20x+100=0

$x^{2} + 20 x + 100 = 0$

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 $a = 1$ , $b = 20$ , and $c = 100$ into the quadratic formula and solve for $x$ .

$\frac{- 20 \pm \sqrt{20^{2} - 4 \cdot (1 \cdot 100)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $20$ to the power of $2$ .

$x = \frac{- 20 \pm \sqrt{400 - 4 \cdot 1 \cdot 100}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 100$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 20 \pm \sqrt{400 - 4 \cdot 100}}{2 \cdot 1}$

Multiply $- 4$ by $100$ .

$x = \frac{- 20 \pm \sqrt{400 - 400}}{2 \cdot 1}$

Subtract $400$ from $400$ .

$x = \frac{- 20 \pm \sqrt{0}}{2 \cdot 1}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 20 \pm \sqrt{0^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 20 \pm 0}{2 \cdot 1}$

$- 20$ plus or minus $0$ is $- 20$ .

$x = \frac{- 20}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 20}{2}$

Divide $- 20$ by $2$ .

$x = - 10$

Step 4

The final answer is the combination of both solutions.

$x = - 10$ Double roots