Solve Using the Quadratic Formula r^2-9r-38=-9

$r^{2} - 9 r - 38 = - 9$

Step 1

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

Add $9$ to both sides of the equation.

$r^{2} - 9 r - 38 + 9 = 0$

Add $- 38$ and $9$ .

$r^{2} - 9 r - 29 = 0$

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 $a = 1$ , $b = - 9$ , and $c = - 29$ into the quadratic formula and solve for $r$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (1 \cdot - 29)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$r = \frac{9 \pm \sqrt{81 - 4 \cdot 1 \cdot - 29}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 29$ .

Multiply $- 4$ by $1$ .

$r = \frac{9 \pm \sqrt{81 - 4 \cdot - 29}}{2 \cdot 1}$

Multiply $- 4$ by $- 29$ .

$r = \frac{9 \pm \sqrt{81 + 116}}{2 \cdot 1}$

Add $81$ and $116$ .

$r = \frac{9 \pm \sqrt{197}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$r = \frac{9 \pm \sqrt{197}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = \frac{9 \pm \sqrt{197}}{2}$

Decimal Form:

$r = 11.51783442 \dots, - 2.51783442 \dots$