To check if the student is correct, we are going to solve the equation step by step.
Step 1 divide both sides of the equation by 5:
[tex] 5x^2=20 [/tex]
[tex] \frac{5x^2}{5} =\frac{20}{5} [/tex]
[tex] x^2=4 [/tex]
Step 2 take square root to both sides of the equation:
[tex] \sqrt{x^2} =(+/-)\sqrt{4} [/tex]
[tex] x=(+/-)\sqrt{4} [/tex]
[tex] x=2 [/tex] or [tex] x=-2 [/tex]
The equation has tow solutions, [tex] x=2 [/tex] and [tex] x=-2 [/tex].
I disagree with the student because [tex] x=2 [/tex] is just one solution and not the only one; [tex] x=-2 [/tex] is also a valid solution of the equation.
