Solve Using the Quadratic Formula 28x^2-28x+7=0

$28 x^{2} - 28 x + 7 = 0$

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 $a = 28$ , $b = - 28$ , and $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{28 \pm \sqrt{{(- 28)}^{2} - 4 \cdot (28 \cdot 7)}}{2 \cdot 28}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 28$ to the power of $2$ .

$x = \frac{28 \pm \sqrt{784 - 4 \cdot 28 \cdot 7}}{2 \cdot 28}$

Multiply $- 4 \cdot 28 \cdot 7$ .

Multiply $- 4$ by $28$ .

$x = \frac{28 \pm \sqrt{784 - 112 \cdot 7}}{2 \cdot 28}$

Multiply $- 112$ by $7$ .

$x = \frac{28 \pm \sqrt{784 - 784}}{2 \cdot 28}$

Subtract $784$ from $784$ .

$x = \frac{28 \pm \sqrt{0}}{2 \cdot 28}$

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

$x = \frac{28 \pm \sqrt{0^{2}}}{2 \cdot 28}$

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

$x = \frac{28 \pm 0}{2 \cdot 28}$

$28$ plus or minus $0$ is $28$ .

$x = \frac{28}{2 \cdot 28}$

Multiply $2$ by $28$ .

$x = \frac{28}{56}$

Cancel the common factor of $28$ and $56$ .

Factor $28$ out of $28$ .

$x = \frac{28 (1)}{56}$

Cancel the common factors.

Factor $28$ out of $56$ .

$x = \frac{28 \cdot 1}{28 \cdot 2}$

Cancel the common factor.

$x = \frac{28 \cdot 1}{28 \cdot 2}$

Rewrite the expression.

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

Step 4

The final answer is the combination of both solutions.

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