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
disagree with the student, since squaring both positive and negative 2 gives 4, which satisfies the equation after substituting back. the student only identified one of the two valid solutions.
complete
sample response: i disagree. if each side of the equation is divided by 5, the result is $x^2 = 4$. by the square root property of equality, $x = 2$ or $x = -2$. so $x$ could be $-2$ instead of 2?
compare your response with the sample response presented here. did your explanation
□ mention the square root property?
□ say that $x$ could also be $-2$?
done

Explanation:

Step1: Isolate $x^2$ term

Divide both sides by 5:
$\frac{5x^2}{5} = \frac{20}{5}$
Simplify to get $x^2 = 4$

Step2: Solve for $x$

Apply square root property:
$x = \pm\sqrt{4}$
Simplify to get $x = 2$ or $x = -2$

Step3: Evaluate student's claim

Student only identified $x=2$, missing $x=-2$.

Answer:

Disagree with the student. The equation $5x^2=20$ simplifies to $x^2=4$, which has two solutions: $x=2$ and $x=-2$, since both positive and negative values squared equal 4. The student only identified one valid solution.

For the comparison checkboxes:

• $\square$ mention the square root property? (The provided complete response does not explicitly name the square root property, unlike the sample)
• $\checkmark$ say that $x$ could also be $-2$? (The provided complete response states this)