%5E2%3D8.jpeg "(x+3)^2=8")
Solving the Equation (x + 3)^2 = 8
This equation involves a squared term, so we need to use the square root property to solve for x. Here's how to do it:
Step 1: Isolate the Squared Term
The squared term is already isolated on the left side of the equation.
Step 2: Take the Square Root of Both Sides
Taking the square root of both sides will eliminate the square on the left side:
√[(x + 3)^2] = ±√8
Remember: When taking the square root of both sides, we need to consider both positive and negative solutions.
Step 3: Simplify
- Simplify the left side: √[(x + 3)^2] = x + 3
- Simplify the right side: √8 = √(4 * 2) = 2√2
This gives us:
x + 3 = ±2√2
Step 4: Solve for x
Subtract 3 from both sides to isolate x:
x = -3 ± 2√2
Solutions
Therefore, the solutions to the equation (x + 3)^2 = 8 are:
- x = -3 + 2√2
- x = -3 - 2√2