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Question
x^{4}\times x=5x
Solve the equation
x_{1}=-\sqrt[4]{5},x_{2}=0,x_{3}=\sqrt[4]{5}
Alternative Form
x_{1}\approx -1.495349,x_{2}=0,x_{3}\approx 1.495349
Evaluate
x^{4}\times x=5x
Multiply the terms
More Steps
Evaluate
x^{4}\times x
\text{Use the product rule }a^{n}\times a^{m}=a^{n+m}\text{ to simplify the expression}
x^{4+1}
Add the numbers
x^{5}
x^{5}=5x
Move the expression to the left side
x^{5}-5x=0
Factor the expression
x\left(x^{4}-5\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=0\\&x^{4}-5=0\end{align}
Solve the equation
More Steps
Evaluate
x^{4}-5=0
Move the constant to the right-hand side and change its sign
x^{4}=0+5
Removing 0 doesn't change the value,so remove it from the expression
x^{4}=5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt[4]{5}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\sqrt[4]{5}\\&x=-\sqrt[4]{5}\end{align}
\begin{align}&x=0\\&x=\sqrt[4]{5}\\&x=-\sqrt[4]{5}\end{align}
Solution
x_{1}=-\sqrt[4]{5},x_{2}=0,x_{3}=\sqrt[4]{5}
Alternative Form
x_{1}\approx -1.495349,x_{2}=0,x_{3}\approx 1.495349
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