Solve Using the Quadratic Formula x^2-7x=11

$x^{2} - 7 x = 11$

Step 1

Subtract $11$ from both sides of the equation.

$x^{2} - 7 x - 11 = 0$

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 $a = 1$ , $b = - 7$ , and $c = - 11$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (1 \cdot - 11)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 1 \cdot - 11}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 11$ .

Multiply $- 4$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot - 11}}{2 \cdot 1}$

Multiply $- 4$ by $- 11$ .

$x = \frac{7 \pm \sqrt{49 + 44}}{2 \cdot 1}$

Add $49$ and $44$ .

$x = \frac{7 \pm \sqrt{93}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{93}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{93}}{2}$

Decimal Form:

$x = 8.32182538 \dots, - 1.32182538 \dots$