Question

a student says that if $5x^2 = 20$, then $x$ must be equal to 2. do you agree or disagree with the student? justify your answer.

Explanation:

Step1: Solve the equation \(5x^2 = 20\) for \(x\)

First, divide both sides of the equation by 5:
\(\frac{5x^2}{5} = \frac{20}{5}\)
Simplifying, we get \(x^2 = 4\).

Step2: Find the solutions for \(x\)

To solve \(x^2 = 4\), we take the square root of both sides. Remember that the square root of a number can be positive or negative, so:
\(x = \pm\sqrt{4}\)
Simplifying \(\sqrt{4}\) gives 2, so \(x = 2\) or \(x = -2\).

Answer:

I disagree with the student. Solving \(5x^2 = 20\) gives \(x^2 = 4\), so \(x = 2\) or \(x = -2\) (not just \(x = 2\)).