Questions: 2x^3 = 44x

Transcript text: $2 x^{3}=44 x$

Solution

Solution Steps

To solve the equation $2x^3 = 44x$, we can first simplify it by dividing both sides by $x$, assuming $x \neq 0$. This gives us $2x^2 = 44$. We can then solve for $x^2$ and subsequently find the values of $x$.

Step 1: Simplifying the Equation

We start with the equation: \[ 2x^3 = 44x \] Assuming $x \neq 0$, we can divide both sides by $x$: \[ 2x^2 = 44 \]

Step 2: Solving for $x^2$

Next, we simplify the equation: \[ x^2 = \frac{44}{2} = 22 \]

Step 3: Finding the Values of $x$

Taking the square root of both sides, we find: \[ x = \pm \sqrt{22} \] Additionally, we must consider the case when $x = 0$. Thus, the complete set of solutions is: \[ x = 0, \quad x = -\sqrt{22}, \quad x = \sqrt{22} \]

Final Answer

The solutions to the equation are: \[ \boxed{x = 0}, \quad \boxed{x = -\sqrt{22}}, \quad \boxed{x = \sqrt{22}} \]

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