Which of the following is equivalent to (2x-3)^2=25 ?
A) 2x - 3 = 5
B) 2x - 3 = -5
C) 2x - 3 = 5 and 2x - 3 = -5
(-5)^2 or 5^2 = 25. Does that help?
To find the equivalent equation to (2x-3)^2 = 25, we can start by taking the square root of both sides of the equation. This is done to "undo" the squaring operation. However, it is important to consider both the positive and negative square roots since the original equation was squared.
√(2x-3)^2 = ±√25
Simplifying this gives us:
2x - 3 = ±5
Now we can split this equation into two separate equations considering both the positive and negative square roots:
Equation 1: 2x - 3 = 5
Equation 2: 2x - 3 = -5
So the correct answer is:
C) 2x - 3 = 5 and 2x - 3 = -5