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Question
2w^{6}\times 10=30w^{3}
Solve the equation
w_{1}=0,w_{2}=\frac{\sqrt[3]{12}}{2}
Alternative Form
w_{1}=0,w_{2}\approx 1.144714
Evaluate
2w^{6}\times 10=30w^{3}
Multiply the terms
20w^{6}=30w^{3}
Add or subtract both sides
20w^{6}-30w^{3}=0
Factor the expression
10w^{3}\left(2w^{3}-3\right)=0
Divide both sides
w^{3}\left(2w^{3}-3\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&w^{3}=0\\&2w^{3}-3=0\end{align}
The only way a power can be 0 is when the base equals 0
\begin{align}&w=0\\&2w^{3}-3=0\end{align}
Solve the equation
More Steps
Evaluate
2w^{3}-3=0
Move the constant to the right-hand side and change its sign
2w^{3}=0+3
Removing 0 doesn't change the value,so remove it from the expression
2w^{3}=3
Divide both sides
\frac{2w^{3}}{2}=\frac{3}{2}
Divide the numbers
w^{3}=\frac{3}{2}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{w^{3}}=\sqrt[3]{\frac{3}{2}}
Calculate
w=\sqrt[3]{\frac{3}{2}}
Simplify the root
More Steps
Evaluate
\sqrt[3]{\frac{3}{2}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{3}}{\sqrt[3]{2}}
Multiply by the Conjugate
\frac{\sqrt[3]{3}\times \sqrt[3]{2^{2}}}{\sqrt[3]{2}\times \sqrt[3]{2^{2}}}
Simplify
\frac{\sqrt[3]{3}\times \sqrt[3]{4}}{\sqrt[3]{2}\times \sqrt[3]{2^{2}}}
Multiply the numbers
\frac{\sqrt[3]{12}}{\sqrt[3]{2}\times \sqrt[3]{2^{2}}}
Multiply the numbers
\frac{\sqrt[3]{12}}{2}
w=\frac{\sqrt[3]{12}}{2}
\begin{align}&w=0\\&w=\frac{\sqrt[3]{12}}{2}\end{align}
Solution
w_{1}=0,w_{2}=\frac{\sqrt[3]{12}}{2}
Alternative Form
w_{1}=0,w_{2}\approx 1.144714
Show Solutions
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