Solve Using the Quadratic Formula 36x^2-60x+25=0

$36 x^{2} - 60 x + 25 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 36$ , $b = - 60$ , and $c = 25$ into the quadratic formula and solve for $x$ .

$\frac{60 \pm \sqrt{{(- 60)}^{2} - 4 \cdot (36 \cdot 25)}}{2 \cdot 36}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 60$ to the power of $2$ .

$x = \frac{60 \pm \sqrt{3600 - 4 \cdot 36 \cdot 25}}{2 \cdot 36}$

Multiply $- 4 \cdot 36 \cdot 25$ .

Multiply $- 4$ by $36$ .

$x = \frac{60 \pm \sqrt{3600 - 144 \cdot 25}}{2 \cdot 36}$

Multiply $- 144$ by $25$ .

$x = \frac{60 \pm \sqrt{3600 - 3600}}{2 \cdot 36}$

Subtract $3600$ from $3600$ .

$x = \frac{60 \pm \sqrt{0}}{2 \cdot 36}$

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

$x = \frac{60 \pm \sqrt{0^{2}}}{2 \cdot 36}$

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

$x = \frac{60 \pm 0}{2 \cdot 36}$

$60$ plus or minus $0$ is $60$ .

$x = \frac{60}{2 \cdot 36}$

Multiply $2$ by $36$ .

$x = \frac{60}{72}$

Cancel the common factor of $60$ and $72$ .

Factor $12$ out of $60$ .

$x = \frac{12 (5)}{72}$

Cancel the common factors.

Factor $12$ out of $72$ .

$x = \frac{12 \cdot 5}{12 \cdot 6}$

Cancel the common factor.

$x = \frac{12 \cdot 5}{12 \cdot 6}$

Rewrite the expression.

$x = \frac{5}{6}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{5}{6}$ Double roots