Solve Using the Quadratic Formula 4x^2-28x=-11

$4 x^{2} - 28 x = - 11$

Step 1

Add $11$ to both sides of the equation.

$4 x^{2} - 28 x + 11 = 0$

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 $a = 4$ , $b = - 28$ , and $c = 11$ into the quadratic formula and solve for $x$ .

$\frac{28 \pm \sqrt{{(- 28)}^{2} - 4 \cdot (4 \cdot 11)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 28$ to the power of $2$ .

$x = \frac{28 \pm \sqrt{784 - 4 \cdot 4 \cdot 11}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{28 \pm \sqrt{784 - 16 \cdot 11}}{2 \cdot 4}$

Multiply $- 16$ by $11$ .

$x = \frac{28 \pm \sqrt{784 - 176}}{2 \cdot 4}$

Subtract $176$ from $784$ .

$x = \frac{28 \pm \sqrt{608}}{2 \cdot 4}$

Rewrite $608$ as $4^{2} \cdot 38$ .

Factor $16$ out of $608$ .

$x = \frac{28 \pm \sqrt{16 (38)}}{2 \cdot 4}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{28 \pm \sqrt{4^{2} \cdot 38}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{28 \pm 4 \sqrt{38}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{28 \pm 4 \sqrt{38}}{8}$

Simplify $\frac{28 \pm 4 \sqrt{38}}{8}$ .

$x = \frac{7 \pm \sqrt{38}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{38}}{2}$

Decimal Form:

$x = 6.58220700 \dots, 0.41779299 \dots$