Question

Solve (2x – 1)^2 = 9.

A)  x = –2, –1

B)  x = 2, –1

C)  x = 2, 1

D)  x = –2, 1

Answer 1

B

Explanation:

First, we can see that the equation on the left is getting squared, and that we need it to equal a positive number. When any number is squared, no matter if it's positive or negative, it comes out positive.

Next, let's think of our perfect squares.

`1^(2)` = 1

`2^(2)` = 4

`3^(2)` = 9

Now look back on the underlined sentence. So we now know that we need our equation on the left to equal either -3 or 3.

`(2(2) - 1)^(2)` = 9

`(4 - 1)^(2)` = 9

`(3)^(2)` = 9
9 = 9

Now we know that our positive number is 2. Let's look for our negative.

`(2(-1) - 1)^(2)` = 9

`(-2 - 1)^(2)` = 9

`(-3)^(2)` = 9
9 = 9

Now we know that our x is both 2 and -1.

Answer 2

To solve the equation (2x – 1)^2 = 9, you can follow these steps:

1. Take the square root of both sides to isolate (2x – 1):
√[(2x – 1)^2] = √9

2. Simplify:
2x – 1 = ±3

3. Add 1 to both sides of the equation:
2x = 1 ± 3

4. Divide by 2:
x = (1 ± 3)/2

Now, you have two possible solutions:

x = (1 + 3)/2 = 4/2 = 2
x = (1 - 3)/2 = -2/2 = -1

So, the solutions are:

C) x = 2, 1