Solve Using the Quadratic Formula 4x^2-8x=-4

$4 x^{2} - 8 x = - 4$

Step 1

Add $4$ to both sides of the equation.

$4 x^{2} - 8 x + 4 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 4$ , $b = - 8$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (4 \cdot 4)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 4 \cdot 4}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot 4$ .

Multiply $- 4$ by $4$ .

$x = \frac{8 \pm \sqrt{64 - 16 \cdot 4}}{2 \cdot 4}$

Multiply $- 16$ by $4$ .

$x = \frac{8 \pm \sqrt{64 - 64}}{2 \cdot 4}$

Subtract $64$ from $64$ .

$x = \frac{8 \pm \sqrt{0}}{2 \cdot 4}$

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

$x = \frac{8 \pm \sqrt{0^{2}}}{2 \cdot 4}$

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

$x = \frac{8 \pm 0}{2 \cdot 4}$

$8$ plus or minus $0$ is $8$ .

$x = \frac{8}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{8}{8}$

Divide $8$ by $8$ .

$x = 1$

Step 5

The final answer is the combination of both solutions.

$x = 1$ Double roots