Type a math problem or upload a photo, screenshot, handwritten question...
error msg
- Differential
- Integral
- Trigonometry
- Letters
- Algebra
- Calculus
- Trigonometry
- Matrix
Question
3x^{5}=2x
Solve the equation
x_{1}=-\frac{\sqrt[4]{54}}{3},x_{2}=0,x_{3}=\frac{\sqrt[4]{54}}{3}
Alternative Form
x_{1}\approx -0.903602,x_{2}=0,x_{3}\approx 0.903602
Evaluate
3x^{5}=2x
Add or subtract both sides
3x^{5}-2x=0
Factor the expression
x\left(3x^{4}-2\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=0\\&3x^{4}-2=0\end{align}
Solve the equation
More Steps
Evaluate
3x^{4}-2=0
Move the constant to the right-hand side and change its sign
3x^{4}=0+2
Removing 0 doesn't change the value,so remove it from the expression
3x^{4}=2
Divide both sides
\frac{3x^{4}}{3}=\frac{2}{3}
Divide the numbers
x^{4}=\frac{2}{3}
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt[4]{\frac{2}{3}}
Simplify the expression
More Steps
Evaluate
\sqrt[4]{\frac{2}{3}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[4]{2}}{\sqrt[4]{3}}
Multiply by the Conjugate
\frac{\sqrt[4]{2}\times \sqrt[4]{3^{3}}}{\sqrt[4]{3}\times \sqrt[4]{3^{3}}}
Simplify
\frac{\sqrt[4]{2}\times \sqrt[4]{27}}{\sqrt[4]{3}\times \sqrt[4]{3^{3}}}
Multiply the numbers
\frac{\sqrt[4]{54}}{\sqrt[4]{3}\times \sqrt[4]{3^{3}}}
Multiply the numbers
\frac{\sqrt[4]{54}}{3}
x=\pm \frac{\sqrt[4]{54}}{3}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{\sqrt[4]{54}}{3}\\&x=-\frac{\sqrt[4]{54}}{3}\end{align}
\begin{align}&x=0\\&x=\frac{\sqrt[4]{54}}{3}\\&x=-\frac{\sqrt[4]{54}}{3}\end{align}
Solution
x_{1}=-\frac{\sqrt[4]{54}}{3},x_{2}=0,x_{3}=\frac{\sqrt[4]{54}}{3}
Alternative Form
x_{1}\approx -0.903602,x_{2}=0,x_{3}\approx 0.903602
Show Solutions
Graph
