Solve Using the Quadratic Formula -25x^2+20x-4=0

$- 25 x^{2} + 20 x - 4 = 0$

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 $a = - 25$ , $b = 20$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{- 20 \pm \sqrt{20^{2} - 4 \cdot (- 25 \cdot - 4)}}{2 \cdot - 25}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 20 \pm \sqrt{400 - 4 \cdot - 25 \cdot - 4}}{2 \cdot - 25}$

Multiply $- 4 \cdot - 25 \cdot - 4$ .

Multiply $- 4$ by $- 25$ .

$x = \frac{- 20 \pm \sqrt{400 + 100 \cdot - 4}}{2 \cdot - 25}$

Multiply $100$ by $- 4$ .

$x = \frac{- 20 \pm \sqrt{400 - 400}}{2 \cdot - 25}$

Subtract $400$ from $400$ .

$x = \frac{- 20 \pm \sqrt{0}}{2 \cdot - 25}$

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

$x = \frac{- 20 \pm \sqrt{0^{2}}}{2 \cdot - 25}$

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

$x = \frac{- 20 \pm 0}{2 \cdot - 25}$

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

$x = \frac{- 20}{2 \cdot - 25}$

Multiply $2$ by $- 25$ .

$x = \frac{- 20}{- 50}$

Cancel the common factor of $- 20$ and $- 50$ .

Factor $- 10$ out of $- 20$ .

$x = \frac{- 10 \cdot 2}{- 50}$

Cancel the common factors.

Factor $- 10$ out of $- 50$ .

$x = \frac{- 10 \cdot 2}{- 10 \cdot 5}$

Cancel the common factor.

$x = \frac{- 10 \cdot 2}{- 10 \cdot 5}$

Rewrite the expression.

$x = \frac{2}{5}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{2}{5}$ Double roots