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(x+2)^2-3=1

less than a minute read Jun 16, 2024
(x+2)^2-3=1

Solving the Equation: (x+2)^2 - 3 = 1

This article will walk through the steps involved in solving the equation (x+2)^2 - 3 = 1.

Step 1: Isolate the Squared Term

  • Add 3 to both sides of the equation: (x+2)^2 - 3 + 3 = 1 + 3
  • Simplify: (x+2)^2 = 4

Step 2: Take the Square Root of Both Sides

  • Apply the square root operation to both sides: √[(x+2)^2] = ±√4
  • Simplify: x + 2 = ±2

Step 3: Solve for x

  • Isolate x by subtracting 2 from both sides: x + 2 - 2 = ±2 - 2
  • Simplify: x = -2 ± 2

Step 4: Calculate the Solutions

  • Calculate the positive solution: x = -2 + 2 = 0
  • Calculate the negative solution: x = -2 - 2 = -4

Conclusion

Therefore, the solutions to the equation (x+2)^2 - 3 = 1 are x = 0 and x = -4.

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