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
square root of each side.
2x-3= +- 5
To find which equation is equivalent to (2x-3)^2=25, we need to solve the given equation and see which of the options is true.
First, we can start by taking the square root of both sides of the equation: √[(2x-3)^2] = √25.
This simplifies to: 2x - 3 = ±√25.
Next, we can simplify the square root of 25: 2x - 3 = ±5.
Now, let's examine the options:
A) 2x - 3 = 5.
B) 2x - 3 = -5.
C) 2x - 3 = 5 and 2x - 3 = -5.
To determine which option is correct, we need to substitute the solutions we obtained back into the original equation and check if they are valid.
Let's substitute 2x - 3 = 5 into the original equation:
(2x - 3)^2 = 25.
(5)^2 = 25.
25 = 25.
The equation holds true, so one solution is 2x - 3 = 5.
Now, let's substitute 2x - 3 = -5 into the original equation:
(2x - 3)^2 = 25.
(-5)^2 = 25.
25 = 25.
Again, the equation holds true, so the other solution is 2x - 3 = -5.
Therefore, the correct answer is option C) 2x - 3 = 5 and 2x - 3 = -5.