Solve Using the Quadratic Formula x^2+4=8x+5

$x^{2} + 4 = 8 x + 5$

Step 1

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

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

Subtract $8 x$ from both sides of the equation.

$x^{2} + 4 - 8 x = 5$

Subtract $5$ from both sides of the equation.

$x^{2} + 4 - 8 x - 5 = 0$

Subtract $5$ from $4$ .

$x^{2} - 8 x - 1 = 0$

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 $a = 1$ , $b = - 8$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 1)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 1}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 1}}{2 \cdot 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{8 \pm \sqrt{64 + 4}}{2 \cdot 1}$

Add $64$ and $4$ .

$x = \frac{8 \pm \sqrt{68}}{2 \cdot 1}$

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$x = \frac{8 \pm \sqrt{4 (17)}}{2 \cdot 1}$

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 17}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{17}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 \sqrt{17}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{17}}{2}$ .

$x = 4 \pm \sqrt{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4 \pm \sqrt{17}$

Decimal Form:

$x = 8.12310562 \dots, - 0.12310562 \dots$