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Question
m^{2}\times \frac{3269}{10}-3083
Simplify the expression
\frac{3269}{10}m^{2}-3083
Evaluate
m^{2}\times \frac{3269}{10}-3083
Solution
\frac{3269}{10}m^{2}-3083
Show Solutions
Factor the expression
\frac{1}{10}\left(3269m^{2}-30830\right)
Evaluate
m^{2}\times \frac{3269}{10}-3083
Use the commutative property to reorder the terms
\frac{3269}{10}m^{2}-3083
Solution
\frac{1}{10}\left(3269m^{2}-30830\right)
Show Solutions
Find the roots
m_{1}=-\frac{\sqrt{100783270}}{3269},m_{2}=\frac{\sqrt{100783270}}{3269}
Alternative Form
m_{1}\approx -3.070996,m_{2}\approx 3.070996
Evaluate
m^{2}\times \frac{3269}{10}-3083
To find the roots of the expression,set the expression equal to 0
m^{2}\times \frac{3269}{10}-3083=0
Use the commutative property to reorder the terms
\frac{3269}{10}m^{2}-3083=0
Move the constant to the right-hand side and change its sign
\frac{3269}{10}m^{2}=0+3083
Removing 0 doesn't change the value,so remove it from the expression
\frac{3269}{10}m^{2}=3083
Multiply by the reciprocal
\frac{3269}{10}m^{2}\times \frac{10}{3269}=3083\times \frac{10}{3269}
Multiply
m^{2}=3083\times \frac{10}{3269}
Multiply
More Steps
Evaluate
3083\times \frac{10}{3269}
Multiply the numbers
\frac{3083\times 10}{3269}
Multiply the numbers
\frac{30830}{3269}
m^{2}=\frac{30830}{3269}
Take the root of both sides of the equation and remember to use both positive and negative roots
m=\pm \sqrt{\frac{30830}{3269}}
Simplify the expression
More Steps
Evaluate
\sqrt{\frac{30830}{3269}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt{30830}}{\sqrt{3269}}
Multiply by the Conjugate
\frac{\sqrt{30830}\times \sqrt{3269}}{\sqrt{3269}\times \sqrt{3269}}
Multiply the numbers
More Steps
Evaluate
\sqrt{30830}\times \sqrt{3269}
The product of roots with the same index is equal to the root of the product
\sqrt{30830\times 3269}
Calculate the product
\sqrt{100783270}
\frac{\sqrt{100783270}}{\sqrt{3269}\times \sqrt{3269}}
When a square root of an expression is multiplied by itself,the result is that expression
\frac{\sqrt{100783270}}{3269}
m=\pm \frac{\sqrt{100783270}}{3269}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&m=\frac{\sqrt{100783270}}{3269}\\&m=-\frac{\sqrt{100783270}}{3269}\end{align}
Solution
m_{1}=-\frac{\sqrt{100783270}}{3269},m_{2}=\frac{\sqrt{100783270}}{3269}
Alternative Form
m_{1}\approx -3.070996,m_{2}\approx 3.070996
Show Solutions
