%5E2%3D36.jpeg "(x+3)^2=36")
Solving the Equation (x+3)^2 = 36
This equation involves a squared term, which means we need to consider both positive and negative solutions. Let's break down the steps to solve it:
1. Taking the Square Root
First, we need to isolate the squared term by taking the square root of both sides of the equation:
√((x+3)^2) = ±√36
This gives us:
x + 3 = ±6
2. Isolating x
Next, we need to isolate 'x' by subtracting 3 from both sides:
x = -3 ±6
3. Finding the Solutions
Now, we have two possible solutions:
- x = -3 + 6 = 3
- x = -3 - 6 = -9
Therefore, the solutions to the equation (x+3)^2 = 36 are x = 3 and x = -9.
Verification
We can verify our solutions by plugging them back into the original equation:
- For x = 3: (3 + 3)^2 = 6^2 = 36
- For x = -9: (-9 + 3)^2 = (-6)^2 = 36
Both solutions satisfy the original equation.