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

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

Step 1

Add $3$ to both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 8 \cdot 3}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot 3$ .

Multiply $- 4$ by $8$ .

$x = \frac{11 \pm \sqrt{121 - 32 \cdot 3}}{2 \cdot 8}$

Multiply $- 32$ by $3$ .

$x = \frac{11 \pm \sqrt{121 - 96}}{2 \cdot 8}$

Subtract $96$ from $121$ .

$x = \frac{11 \pm \sqrt{25}}{2 \cdot 8}$

Rewrite $25$ as $5^{2}$ .

$x = \frac{11 \pm \sqrt{5^{2}}}{2 \cdot 8}$

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

$x = \frac{11 \pm 5}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{11 \pm 5}{16}$

Step 5

The final answer is the combination of both solutions.

$x = 1, \frac{3}{8}$