2-%3D-64-responses.jpeg "(x+3)2 = 64 Responses")
Solving the Equation (x + 3)² = 64
This equation is a quadratic equation in disguise, and we can solve it using a few different methods:
Method 1: Square Root Property
-
Take the square root of both sides: √(x + 3)² = ±√64
-
Simplify: x + 3 = ±8
-
Solve for x:
- x + 3 = 8 => x = 5
- x + 3 = -8 => x = -11
Therefore, the solutions to the equation (x + 3)² = 64 are x = 5 and x = -11.
Method 2: Expanding and Solving
-
Expand the left side: x² + 6x + 9 = 64
-
Move all terms to one side: x² + 6x - 55 = 0
-
Factor the quadratic: (x + 11)(x - 5) = 0
-
Set each factor to zero and solve:
- x + 11 = 0 => x = -11
- x - 5 = 0 => x = 5
Again, we arrive at the solutions x = 5 and x = -11.
Verifying the Solutions
We can plug our solutions back into the original equation to verify they are correct:
- For x = 5: (5 + 3)² = 8² = 64 (True)
- For x = -11: (-11 + 3)² = (-8)² = 64 (True)
Both solutions hold true for the original equation.
In summary, the solutions to the equation (x + 3)² = 64 are x = 5 and x = -11.