Solve Using the Quadratic Formula x^2-22x+121=0

$x^{2} - 22 x + 121 = 0$

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 $a = 1$ , $b = - 22$ , and $c = 121$ into the quadratic formula and solve for $x$ .

$\frac{22 \pm \sqrt{{(- 22)}^{2} - 4 \cdot (1 \cdot 121)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 22$ to the power of $2$ .

$x = \frac{22 \pm \sqrt{484 - 4 \cdot 1 \cdot 121}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 121$ .

Multiply $- 4$ by $1$ .

$x = \frac{22 \pm \sqrt{484 - 4 \cdot 121}}{2 \cdot 1}$

Multiply $- 4$ by $121$ .

$x = \frac{22 \pm \sqrt{484 - 484}}{2 \cdot 1}$

Subtract $484$ from $484$ .

$x = \frac{22 \pm \sqrt{0}}{2 \cdot 1}$

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

$x = \frac{22 \pm \sqrt{0^{2}}}{2 \cdot 1}$

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

$x = \frac{22 \pm 0}{2 \cdot 1}$

$22$ plus or minus $0$ is $22$ .

$x = \frac{22}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{22}{2}$

Divide $22$ by $2$ .

$x = 11$

Step 4

The final answer is the combination of both solutions.

$x = 11$ Double roots