Solve : `(2x-3)^(2)=25`.

Answer

To solve the equation \((2x - 3)^2 = 25\), we can follow these steps:

### Step 1: Take the square root of both sides
To eliminate the square on the left side, we take the square root of both sides of the equation:

\[ \sqrt{(2x - 3)^2} = \sqrt{25} \]

### Step 2: Simplify the square root
The square root of a square gives us the absolute value:

\[ |2x - 3| = 5 \]

### Step 3: Set up two equations
The absolute value equation \(|2x - 3| = 5\) leads to two possible cases:

1. \(2x - 3 = 5\)
2. \(2x - 3 = -5\)

### Step 4: Solve the first equation
For the first case:

\[ 2x - 3 = 5 \]

Add 3 to both sides:

\[ 2x = 5 + 3 \]
\[ 2x = 8 \]

Now, divide by 2:

\[ x = \frac{8}{2} = 4 \]

### Step 5: Solve the second equation
For the second case:

\[ 2x - 3 = -5 \]

Add 3 to both sides:

\[ 2x = -5 + 3 \]
\[ 2x = -2 \]

Now, divide by 2:

\[ x = \frac{-2}{2} = -1 \]

### Step 6: Write the final solutions
The solutions to the equation \((2x - 3)^2 = 25\) are:

\[ x = 4 \quad \text{and} \quad x = -1 \]

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