Solve Using the Quadratic Formula x^2-11x+56=5x+13

$x^{2} - 11 x + 56 = 5 x + 13$

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$x^{2} - 11 x + 56 - 5 x = 13$

Subtract $13$ from both sides of the equation.

$x^{2} - 11 x + 56 - 5 x - 13 = 0$

Simplify $x^{2} - 11 x + 56 - 5 x - 13$ .

Subtract $5 x$ from $- 11 x$ .

$x^{2} - 16 x + 56 - 13 = 0$

Subtract $13$ from $56$ .

$x^{2} - 16 x + 43 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 16$ , and $c = 43$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (1 \cdot 43)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 1 \cdot 43}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 43}}{2 \cdot 1}$

Multiply $- 4$ by $43$ .

$x = \frac{16 \pm \sqrt{256 - 172}}{2 \cdot 1}$

Subtract $172$ from $256$ .

$x = \frac{16 \pm \sqrt{84}}{2 \cdot 1}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$x = \frac{16 \pm \sqrt{4 (21)}}{2 \cdot 1}$

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

$x = \frac{16 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{16 \pm 2 \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{16 \pm 2 \sqrt{21}}{2}$

Simplify $\frac{16 \pm 2 \sqrt{21}}{2}$ .

$x = 8 \pm \sqrt{21}$

The result can be shown in multiple forms.

Exact Form:

$x = 8 \pm \sqrt{21}$

Decimal Form:

$x = 12.58257569 \dots, 3.41742430 \dots$