Jesse and Benjamin are asked to solve
100x^2−100=0. Here are their solutions. Who is correct? Explain.
Jesse
100x^2-100=0
(10x)^2-10^2=0
(10x-10)(10x+10)=0
10(x-1)*10(x+1)=0
100(x-1)(x+1)=0
(x-1)=0 or (x+1)=0
x= 1 or x=-1
Benjamin
100x^2-100
=100(x^2-1)
=100(x-1)(x+1)
(x-1)=0 or (x+1)=0
x=1 or x=-1
Both Jesse and Benjamin are correct. They used different methods to solve the equation, but they arrived at the same solutions.
Jesse factored the equation using the difference of squares formula, while Benjamin factored it using the distributive property. Both methods are valid and commonly used in algebra.
Therefore, the solutions x=1 and x=-1 are correct.