Solve Using the Quadratic Formula 9w^2-30w=-25

$9 w^{2} - 30 w = - 25$

Step 1

Add $25$ to both sides of the equation.

$9 w^{2} - 30 w + 25 = 0$

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 $a = 9$ , $b = - 30$ , and $c = 25$ into the quadratic formula and solve for $w$ .

$\frac{30 \pm \sqrt{{(- 30)}^{2} - 4 \cdot (9 \cdot 25)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 30$ to the power of $2$ .

$w = \frac{30 \pm \sqrt{900 - 4 \cdot 9 \cdot 25}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot 25$ .

Multiply $- 4$ by $9$ .

$w = \frac{30 \pm \sqrt{900 - 36 \cdot 25}}{2 \cdot 9}$

Multiply $- 36$ by $25$ .

$w = \frac{30 \pm \sqrt{900 - 900}}{2 \cdot 9}$

Subtract $900$ from $900$ .

$w = \frac{30 \pm \sqrt{0}}{2 \cdot 9}$

Rewrite $0$ as $0^{2}$ .

$w = \frac{30 \pm \sqrt{0^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$w = \frac{30 \pm 0}{2 \cdot 9}$

$30$ plus or minus $0$ is $30$ .

$w = \frac{30}{2 \cdot 9}$

Multiply $2$ by $9$ .

$w = \frac{30}{18}$

Cancel the common factor of $30$ and $18$ .

Factor $6$ out of $30$ .

$w = \frac{6 (5)}{18}$

Cancel the common factors.

Factor $6$ out of $18$ .

$w = \frac{6 \cdot 5}{6 \cdot 3}$

Cancel the common factor.

$w = \frac{6 \cdot 5}{6 \cdot 3}$

Rewrite the expression.

$w = \frac{5}{3}$

Step 5

The final answer is the combination of both solutions.

$w = \frac{5}{3}$ Double roots