Solve $2x^2 = 10x$

Understand the Problem

The question is asking to solve the equation $2x^2 = 10x$ for the variable $x$. This involves manipulating the equation to isolate $x$ or using algebraic techniques to find the values of $x$ that satisfy the equation.

Answer

$x = 0, 5$

Steps to Solve

Rearrange the equation

Subtract $10x$ from both sides of the equation to set it to zero.

$2x^2 - 10x = 0$

Factor out the common factor

Factor out $2x$ from the left side of the equation.

$2x(x - 5) = 0$

Set each factor to zero

Set each factor equal to zero and solve for $x$.

$2x = 0$ or $x - 5 = 0$

Solve for x

Solve each equation for $x$.

For $2x = 0$: $x = \frac{0}{2} = 0$

For $x - 5 = 0$: $x = 5$

$x = 0, 5$

More Information

The equation $2x^2 = 10x$ has two solutions: $x = 0$ and $x = 5$.

Tips

A common mistake is to divide both sides of the equation by $x$ early on. This would lead to only finding the solution $x=5$, and losing the solution $x=0$. Instead, rearrange the equation so that one side is zero, and then factorize.

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