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Solving the Equation (x+3)^2 = 16
This equation represents a quadratic equation in disguise. Let's break down the steps to solve for x:
1. Take the Square Root of Both Sides
The first step is to isolate the squared term. We can do this by taking the square root of both sides of the equation:
√((x+3)²) = ±√16
This gives us:
x + 3 = ±4
2. Solve for x
Now we have two separate equations to solve:
- Equation 1: x + 3 = 4
- Equation 2: x + 3 = -4
Solving for x in each equation:
- Equation 1: x = 4 - 3 = 1
- Equation 2: x = -4 - 3 = -7
3. Solution
Therefore, the solutions to the equation (x+3)² = 16 are:
x = 1 and x = -7
These are the two values of x that satisfy the original equation.