%5E2%3D50.jpeg "(x+3)^2=50")
Solving the Equation (x + 3)^2 = 50
This equation involves a squared term, so we need to use the square root property to solve it. Here's how to break it down:
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 of the equation gives us:
√((x + 3)^2) = ±√50
Remember: When taking the square root of both sides, we need to consider both positive and negative solutions.
Step 3: Simplify
Simplifying the square roots, we get:
x + 3 = ±√(25 * 2) x + 3 = ±5√2
Step 4: Isolate x
Subtract 3 from both sides to isolate x:
x = -3 ± 5√2
Solutions
Therefore, the solutions to the equation (x + 3)^2 = 50 are:
- x = -3 + 5√2
- x = -3 - 5√2
These are the two possible values of x that satisfy the original equation.