(x+5)^2=169

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x + 5)² = 169

This equation involves a squared term, which means we need to use the square root property to solve for x. Here's how:

1. Isolate the Squared Term

We already have the squared term isolated on the left side of the equation: (x + 5)² = 169

2. Take the Square Root of Both Sides

Remember that when taking the square root of both sides, we need to consider both positive and negative solutions:

√(x + 5)² = ±√169

3. Simplify

This simplifies to:

x + 5 = ±13

4. Solve for x

Now we have two separate equations to solve:

• Case 1: x + 5 = 13

  • Subtract 5 from both sides: x = 8

• Case 2: x + 5 = -13

  • Subtract 5 from both sides: x = -18

Solution

Therefore, the solutions to the equation (x + 5)² = 169 are x = 8 and x = -18.