Solve Using the Quadratic Formula 11x^2+8x-3=0

$11 x^{2} + 8 x - 3 = 0$

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 $a = 11$ , $b = 8$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (11 \cdot - 3)}}{2 \cdot 11}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot 11 \cdot - 3}}{2 \cdot 11}$

Multiply $- 4 \cdot 11 \cdot - 3$ .

Multiply $- 4$ by $11$ .

$x = \frac{- 8 \pm \sqrt{64 - 44 \cdot - 3}}{2 \cdot 11}$

Multiply $- 44$ by $- 3$ .

$x = \frac{- 8 \pm \sqrt{64 + 132}}{2 \cdot 11}$

Add $64$ and $132$ .

$x = \frac{- 8 \pm \sqrt{196}}{2 \cdot 11}$

Rewrite $196$ as $14^{2}$ .

$x = \frac{- 8 \pm \sqrt{14^{2}}}{2 \cdot 11}$

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

$x = \frac{- 8 \pm 14}{2 \cdot 11}$

Multiply $2$ by $11$ .

$x = \frac{- 8 \pm 14}{22}$

Simplify $\frac{- 8 \pm 14}{22}$ .

$x = \frac{- 4 \pm 7}{11}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{3}{11}, - 1$