Question

What is the answer to 9m^2-66m+21=0

Answer 1

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the given quadratic equation.

`9m^2-66m_{}+21=0`

STEP 2: Write the quadratic formula

`(m_1,m_2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

STEP 3: Solve the given equation using the quadratic formula

`\begin{gathered} 9m^2-66m_{}+21 \\ \text{From the }equation, \\ a=9,b=-66,c=21 \\ m_(1,\: 2)=(-\left(-66\right)\pm√(\left(-66\right)^2-4\cdot\:9\cdot\:21))/(2\cdot\:9) \\ Simplify\sqrt[]{(-66)^2-4\cdot\: 9\cdot\: 21} \\ \sqrt[]{(-66)^2-4\cdot\: 9\cdot\: 21}=\sqrt[]{4356-756}=\sqrt[]{3600}=60 \\ \\ m_(1,\: 2)=(-\left(-66\right)\pm\:60)/(2\cdot\:9) \\ Separate\: the\: solutions \\ m_1=(-\left(-66\right)+60)/(2\cdot\:9),\: m_2=(-\left(-66\right)-60)/(2\cdot\:9) \\ m_1=(-(-66)+60)/(2\cdot\: 9)=(66+60)/(18)=(126)/(18)=7 \\ \: m_2=(-(-66)-60)/(2\cdot\: 9)=(66-60)/(18)=(6)/(18)=(1)/(3) \end{gathered}`

Hence, the answer to the given quadratic equation is:

`\begin{gathered} m=7 \\ m=(1)/(3) \end{gathered}`