Question

How do you solve \[5{{x}^{3}}-320x=0\]?

Answer 1

Hint: In this problem, we have to solve and find the value of x from the given equation. We can first add 320x on both sides of the equation. We can then divide 5x on both sides of the equation. We can then take the square root on both sides, where the square and the square root get cancelled on the left-hand side and we can write the perfect square number for the given number on the right-hand side to get the value of x.

Complete step by step answer:
We know that the given equation to be solved is,
\[5{{x}^{3}}-320x=0\]
We can first add 320x on both the left-hand side and the right-hand side of the equation, we get
\[\begin{align}
  & \Rightarrow 5{{x}^{3}}-320x+320x=320x \\
 & \Rightarrow 5{{x}^{3}}=320x \\
\end{align}\]
We can now divide 5x on both the left-hand side and the right-hand side of the equation, we get
\[\Rightarrow \dfrac{5{{x}^{3}}}{5}=\dfrac{320x}{5x}\]
We can now cancel the similar terms, we get
\[\Rightarrow {{x}^{2}}=64\]
We can now take square root on both sides, we get
\[\begin{align}
  & \Rightarrow \sqrt{{{x}^{2}}}=\sqrt{64} \\
 & \Rightarrow \sqrt{{{x}^{2}}}=\sqrt{{{8}^{2}}} \\
\end{align}\]
We can now cancel the square and the square root on both the left-hand side and the right-hand side, we get
\[\Rightarrow x=\pm 8\]

Therefore, the value of \[x=\pm 8\] and 0(because we cancelled out one factor).

Note: Students make mistakes while writing the square term of the number, we should remember some perfect square numbers to substitute in these types of problems. We should also remember that we should write the plus or minus symbol while cancelling the square and the square root.