Solve Using the Quadratic Formula 25x^2-40x=-16

$25 x^{2} - 40 x = - 16$

Step 1

Add $16$ to both sides of the equation.

$25 x^{2} - 40 x + 16 = 0$

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 $a = 25$ , $b = - 40$ , and $c = 16$ into the quadratic formula and solve for $x$ .

$\frac{40 \pm \sqrt{{(- 40)}^{2} - 4 \cdot (25 \cdot 16)}}{2 \cdot 25}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 40$ to the power of $2$ .

$x = \frac{40 \pm \sqrt{1600 - 4 \cdot 25 \cdot 16}}{2 \cdot 25}$

Multiply $- 4 \cdot 25 \cdot 16$ .

Multiply $- 4$ by $25$ .

$x = \frac{40 \pm \sqrt{1600 - 100 \cdot 16}}{2 \cdot 25}$

Multiply $- 100$ by $16$ .

$x = \frac{40 \pm \sqrt{1600 - 1600}}{2 \cdot 25}$

Subtract $1600$ from $1600$ .

$x = \frac{40 \pm \sqrt{0}}{2 \cdot 25}$

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

$x = \frac{40 \pm \sqrt{0^{2}}}{2 \cdot 25}$

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

$x = \frac{40 \pm 0}{2 \cdot 25}$

$40$ plus or minus $0$ is $40$ .

$x = \frac{40}{2 \cdot 25}$

Multiply $2$ by $25$ .

$x = \frac{40}{50}$

Cancel the common factor of $40$ and $50$ .

Factor $10$ out of $40$ .

$x = \frac{10 (4)}{50}$

Cancel the common factors.

Factor $10$ out of $50$ .

$x = \frac{10 \cdot 4}{10 \cdot 5}$

Cancel the common factor.

$x = \frac{10 \cdot 4}{10 \cdot 5}$

Rewrite the expression.

$x = \frac{4}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{4}{5}$ Double roots