%5E2%3D10.jpeg "(x+2)^2=10")
Solving the Equation (x + 2)^2 = 10
This equation involves a squared term, which means we need to use the square root property to solve for x. Here's a step-by-step guide:
1. Isolate the Squared Term:
The squared term is already isolated on the left side of the equation.
2. Take the Square Root of Both Sides:
Remember to consider both positive and negative square roots.
√((x + 2)^2) = ±√10
3. Simplify:
x + 2 = ±√10
4. Isolate x:
Subtract 2 from both sides:
x = -2 ±√10
5. The Solutions:
Therefore, the solutions to the equation (x + 2)^2 = 10 are:
- x = -2 + √10
- x = -2 - √10
Understanding the Solutions:
These two solutions represent the two points on the x-axis where the graph of the function y = (x + 2)^2 intersects the horizontal line y = 10.
Important Note:
It is crucial to remember that taking the square root of both sides introduces the possibility of both positive and negative solutions. This is why we have two solutions in this case.