Solve Using the Quadratic Formula 9p^2=-10p+1

$9 p^{2} = - 10 p + 1$

Step 1

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

Add $10 p$ to both sides of the equation.

$9 p^{2} + 10 p = 1$

Subtract $1$ from both sides of the equation.

$9 p^{2} + 10 p - 1 = 0$

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 $a = 9$ , $b = 10$ , and $c = - 1$ into the quadratic formula and solve for $p$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (9 \cdot - 1)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$p = \frac{- 10 \pm \sqrt{100 - 4 \cdot 9 \cdot - 1}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 1$ .

Multiply $- 4$ by $9$ .

$p = \frac{- 10 \pm \sqrt{100 - 36 \cdot - 1}}{2 \cdot 9}$

Multiply $- 36$ by $- 1$ .

$p = \frac{- 10 \pm \sqrt{100 + 36}}{2 \cdot 9}$

Add $100$ and $36$ .

$p = \frac{- 10 \pm \sqrt{136}}{2 \cdot 9}$

Rewrite $136$ as $2^{2} \cdot 34$ .

Factor $4$ out of $136$ .

$p = \frac{- 10 \pm \sqrt{4 (34)}}{2 \cdot 9}$

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

$p = \frac{- 10 \pm \sqrt{2^{2} \cdot 34}}{2 \cdot 9}$

Pull terms out from under the radical.

$p = \frac{- 10 \pm 2 \sqrt{34}}{2 \cdot 9}$

Multiply $2$ by $9$ .

$p = \frac{- 10 \pm 2 \sqrt{34}}{18}$

Simplify $\frac{- 10 \pm 2 \sqrt{34}}{18}$ .

$p = \frac{- 5 \pm \sqrt{34}}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{- 5 \pm \sqrt{34}}{9}$

Decimal Form:

$p = 0.09232798 \dots, - 1.20343909 \dots$