(x+4)2=25

2 min read Jun 16, 2024
(x+4)2=25

Solving the Equation: (x + 4)² = 25

This equation involves a squared term, making it a quadratic equation. Here's how to solve it:

1. Take the Square Root of Both Sides

Since the left side of the equation is squared, we can isolate the variable by taking the square root of both sides:

√(x + 4)² = ±√25

2. Simplify

The square root of (x + 4)² is simply (x + 4), and the square root of 25 is 5. Remember, when taking the square root, we need to consider both positive and negative values:

x + 4 = ±5

3. Solve for x

Now we have two separate equations:

  • x + 4 = 5
  • x + 4 = -5

Solving the first equation: Subtract 4 from both sides: x = 5 - 4 x = 1

Solving the second equation: Subtract 4 from both sides: x = -5 - 4 x = -9

Solution

Therefore, the solutions to the equation (x + 4)² = 25 are:

x = 1 and x = -9