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Question
x^{6}\times 70-48x
Simplify the expression
70x^{6}-48x
Evaluate
x^{6}\times 70-48x
Solution
70x^{6}-48x
Show Solutions
Factor the expression
2x\left(35x^{5}-24\right)
Evaluate
x^{6}\times 70-48x
Use the commutative property to reorder the terms
70x^{6}-48x
Rewrite the expression
2x\times 35x^{5}-2x\times 24
Solution
2x\left(35x^{5}-24\right)
Show Solutions
Find the roots
x_{1}=0,x_{2}=\frac{\sqrt[5]{24\times 35^{4}}}{35}
Alternative Form
x_{1}=0,x_{2}\approx 0.927318
Evaluate
x^{6}\times 70-48x
To find the roots of the expression,set the expression equal to 0
x^{6}\times 70-48x=0
Use the commutative property to reorder the terms
70x^{6}-48x=0
Factor the expression
2x\left(35x^{5}-24\right)=0
Divide both sides
x\left(35x^{5}-24\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=0\\&35x^{5}-24=0\end{align}
Solve the equation
More Steps
Evaluate
35x^{5}-24=0
Move the constant to the right-hand side and change its sign
35x^{5}=0+24
Removing 0 doesn't change the value,so remove it from the expression
35x^{5}=24
Divide both sides
\frac{35x^{5}}{35}=\frac{24}{35}
Divide the numbers
x^{5}=\frac{24}{35}
\text{Take the }5\text{-th root on both sides of the equation}
\sqrt[5]{x^{5}}=\sqrt[5]{\frac{24}{35}}
Calculate
x=\sqrt[5]{\frac{24}{35}}
Simplify the root
More Steps
Evaluate
\sqrt[5]{\frac{24}{35}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[5]{24}}{\sqrt[5]{35}}
Multiply by the Conjugate
\frac{\sqrt[5]{24}\times \sqrt[5]{35^{4}}}{\sqrt[5]{35}\times \sqrt[5]{35^{4}}}
The product of roots with the same index is equal to the root of the product
\frac{\sqrt[5]{24\times 35^{4}}}{\sqrt[5]{35}\times \sqrt[5]{35^{4}}}
Multiply the numbers
\frac{\sqrt[5]{24\times 35^{4}}}{35}
x=\frac{\sqrt[5]{24\times 35^{4}}}{35}
\begin{align}&x=0\\&x=\frac{\sqrt[5]{24\times 35^{4}}}{35}\end{align}
Solution
x_{1}=0,x_{2}=\frac{\sqrt[5]{24\times 35^{4}}}{35}
Alternative Form
x_{1}=0,x_{2}\approx 0.927318
Show Solutions
