%5E2%3D9.jpeg "(2x+1)^2=9")
Solving the Equation: (2x + 1)² = 9
This equation involves a squared term, which means we need to use a few steps to isolate the variable 'x'. Let's break down the solution:
1. Take the Square Root of Both Sides
To get rid of the square, we take the square root of both sides of the equation:
√(2x + 1)² = ±√9
This gives us two possible solutions because the square root of a number can be positive or negative.
2. Simplify
Simplifying the equation, we have:
2x + 1 = ±3
3. Solve for x
Now we have two separate equations to solve:
- Equation 1: 2x + 1 = 3
- Equation 2: 2x + 1 = -3
Solving Equation 1:
- Subtract 1 from both sides: 2x = 2
- Divide both sides by 2: x = 1
Solving Equation 2:
- Subtract 1 from both sides: 2x = -4
- Divide both sides by 2: x = -2
Conclusion
Therefore, the solutions to the equation (2x + 1)² = 9 are x = 1 and x = -2.