PSAT Math Grid-Ins Question 118: Answer and Explanation
Question: 118
What is the product of all solutions to (x + 2)2 = (2x - 3)2?
Correct Answer: 5/3
Explanation:
Both sides of the equation are squared:
(x + 2)(x + 2) = (2x - 3)(2x - 3)
If you FOIL both sides:
x2 + 4x + 4 = 4x2 - 12x + 9
To find the solutions, you want to get everything on one side. Moving all terms on the left-hand side to the right side of the equation by subtracting gives:
0 = 3x2 - 16x + 5
If you don't see that it can be factored as (3x - 1)(x - 5), then use the quadratic formula:
Therefore, 
or x = 5.
The question asks for the product of all of the solutions, so the answer is
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