Solve Using the Quadratic Formula 25x^2-20x-6=0

$25 x^{2} - 20 x - 6 = 0$

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 $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{20 \pm \sqrt{{(- 20)}^{2} - 4 \cdot (25 \cdot - 6)}}{2 \cdot 25}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{20 \pm \sqrt{400 - 4 \cdot 25 \cdot - 6}}{2 \cdot 25}$

Multiply $- 4 \cdot 25 \cdot - 6$ .

Multiply $- 4$ by $25$ .

$x = \frac{20 \pm \sqrt{400 - 100 \cdot - 6}}{2 \cdot 25}$

Multiply $- 100$ by $- 6$ .

$x = \frac{20 \pm \sqrt{400 + 600}}{2 \cdot 25}$

Add $400$ and $600$ .

$x = \frac{20 \pm \sqrt{1000}}{2 \cdot 25}$

Rewrite $1000$ as $10^{2} \cdot 10$ .

Factor $100$ out of $1000$ .

$x = \frac{20 \pm \sqrt{100 (10)}}{2 \cdot 25}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{20 \pm \sqrt{10^{2} \cdot 10}}{2 \cdot 25}$

Pull terms out from under the radical.

$x = \frac{20 \pm 10 \sqrt{10}}{2 \cdot 25}$

Multiply $2$ by $25$ .

$x = \frac{20 \pm 10 \sqrt{10}}{50}$

Simplify $\frac{20 \pm 10 \sqrt{10}}{50}$ .

$x = \frac{2 \pm \sqrt{10}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2 \pm \sqrt{10}}{5}$

Decimal Form:

$x = 1.03245553 \dots, - 0.23245553 \dots$