Solve Using the Quadratic Formula 44x^2-44x+11=0

$44 x^{2} - 44 x + 11 = 0$

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 $a = 44$ , $b = - 44$ , and $c = 11$ into the quadratic formula and solve for $x$ .

$\frac{44 \pm \sqrt{{(- 44)}^{2} - 4 \cdot (44 \cdot 11)}}{2 \cdot 44}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 44$ to the power of $2$ .

$x = \frac{44 \pm \sqrt{1936 - 4 \cdot 44 \cdot 11}}{2 \cdot 44}$

Multiply $- 4 \cdot 44 \cdot 11$ .

Multiply $- 4$ by $44$ .

$x = \frac{44 \pm \sqrt{1936 - 176 \cdot 11}}{2 \cdot 44}$

Multiply $- 176$ by $11$ .

$x = \frac{44 \pm \sqrt{1936 - 1936}}{2 \cdot 44}$

Subtract $1936$ from $1936$ .

$x = \frac{44 \pm \sqrt{0}}{2 \cdot 44}$

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

$x = \frac{44 \pm \sqrt{0^{2}}}{2 \cdot 44}$

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

$x = \frac{44 \pm 0}{2 \cdot 44}$

$44$ plus or minus $0$ is $44$ .

$x = \frac{44}{2 \cdot 44}$

Multiply $2$ by $44$ .

$x = \frac{44}{88}$

Cancel the common factor of $44$ and $88$ .

Factor $44$ out of $44$ .

$x = \frac{44 (1)}{88}$

Cancel the common factors.

Factor $44$ out of $88$ .

$x = \frac{44 \cdot 1}{44 \cdot 2}$

Cancel the common factor.

$x = \frac{44 \cdot 1}{44 \cdot 2}$

Rewrite the expression.

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

Step 4

The final answer is the combination of both solutions.

$x = \frac{1}{2}$ Double roots