Solve Using the Quadratic Formula 12x^2-11x=11

$12 x^{2} - 11 x = 11$

Step 1

Subtract $11$ from both sides of the equation.

$12 x^{2} - 11 x - 11 = 0$

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 $a = 12$ , $b = - 11$ , and $c = - 11$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (12 \cdot - 11)}}{2 \cdot 12}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 12 \cdot - 11}}{2 \cdot 12}$

Multiply $- 4 \cdot 12 \cdot - 11$ .

Multiply $- 4$ by $12$ .

$x = \frac{11 \pm \sqrt{121 - 48 \cdot - 11}}{2 \cdot 12}$

Multiply $- 48$ by $- 11$ .

$x = \frac{11 \pm \sqrt{121 + 528}}{2 \cdot 12}$

Add $121$ and $528$ .

$x = \frac{11 \pm \sqrt{649}}{2 \cdot 12}$

Multiply $2$ by $12$ .

$x = \frac{11 \pm \sqrt{649}}{24}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11 \pm \sqrt{649}}{24}$

Decimal Form:

$x = 1.51981160 \dots, - 0.60314493 \dots$