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Question
x^{2}-6x^{5}
Factor the expression
x^{2}\left(1-6x^{3}\right)
Evaluate
x^{2}-6x^{5}
Rewrite the expression
x^{2}-x^{2}\times 6x^{3}
Solution
x^{2}\left(1-6x^{3}\right)
Show Solutions
Find the roots
x_{1}=0,x_{2}=\frac{\sqrt[3]{36}}{6}
Alternative Form
x_{1}=0,x_{2}\approx 0.550321
Evaluate
x^{2}-6x^{5}
To find the roots of the expression,set the expression equal to 0
x^{2}-6x^{5}=0
Factor the expression
x^{2}\left(1-6x^{3}\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x^{2}=0\\&1-6x^{3}=0\end{align}
The only way a power can be 0 is when the base equals 0
\begin{align}&x=0\\&1-6x^{3}=0\end{align}
Solve the equation
More Steps
Evaluate
1-6x^{3}=0
Move the constant to the right-hand side and change its sign
-6x^{3}=0-1
Removing 0 doesn't change the value,so remove it from the expression
-6x^{3}=-1
Change the signs on both sides of the equation
6x^{3}=1
Divide both sides
\frac{6x^{3}}{6}=\frac{1}{6}
Divide the numbers
x^{3}=\frac{1}{6}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{\frac{1}{6}}
Calculate
x=\sqrt[3]{\frac{1}{6}}
Simplify the root
More Steps
Evaluate
\sqrt[3]{\frac{1}{6}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{1}}{\sqrt[3]{6}}
Simplify the radical expression
\frac{1}{\sqrt[3]{6}}
Multiply by the Conjugate
\frac{\sqrt[3]{6^{2}}}{\sqrt[3]{6}\times \sqrt[3]{6^{2}}}
Simplify
\frac{\sqrt[3]{36}}{\sqrt[3]{6}\times \sqrt[3]{6^{2}}}
Multiply the numbers
\frac{\sqrt[3]{36}}{6}
x=\frac{\sqrt[3]{36}}{6}
\begin{align}&x=0\\&x=\frac{\sqrt[3]{36}}{6}\end{align}
Solution
x_{1}=0,x_{2}=\frac{\sqrt[3]{36}}{6}
Alternative Form
x_{1}=0,x_{2}\approx 0.550321
Show Solutions
