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Question
3x^{4}-192x^{2}=0
Solve the equation
x_{1}=-8,x_{2}=0,x_{3}=8
Evaluate
3x^{4}-192x^{2}=0
Factor the expression
3x^{2}\left(x^{2}-64\right)=0
Divide both sides
x^{2}\left(x^{2}-64\right)=0
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x^{2}=0\\&x^{2}-64=0\end{align}
The only way a power can be 0 is when the base equals 0
\begin{align}&x=0\\&x^{2}-64=0\end{align}
Solve the equation
More Steps
Evaluate
x^{2}-64=0
Move the constant to the right-hand side and change its sign
x^{2}=0+64
Removing 0 doesn't change the value,so remove it from the expression
x^{2}=64
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt{64}
Simplify the expression
More Steps
Evaluate
\sqrt{64}
\text{Write the number in exponential form with the base of }8
\sqrt{8^{2}}
\text{Reduce the index of the radical and exponent with }2
8
x=\pm 8
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=8\\&x=-8\end{align}
\begin{align}&x=0\\&x=8\\&x=-8\end{align}
Solution
x_{1}=-8,x_{2}=0,x_{3}=8
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