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(x-7)^2-5=4

2 min read Jun 17, 2024
(x-7)^2-5=4

Solving the Equation: (x-7)^2 - 5 = 4

This article will guide you through the steps to solve the equation (x-7)^2 - 5 = 4.

Step 1: Isolate the squared term

  1. Add 5 to both sides of the equation: (x-7)^2 - 5 + 5 = 4 + 5 This simplifies to: (x-7)^2 = 9

Step 2: Take the square root of both sides

  1. Take the square root of both sides of the equation: √[(x-7)^2] = ±√9
  2. Simplify: x - 7 = ±3

Step 3: Solve for x

  1. Add 7 to both sides of the equation: x - 7 + 7 = ±3 + 7
  2. Simplify: x = 7 ± 3

Step 4: Find the two solutions

  1. Solve for x when the right side is positive: x = 7 + 3 = 10
  2. Solve for x when the right side is negative: x = 7 - 3 = 4

Conclusion

The solutions to the equation (x-7)^2 - 5 = 4 are x = 10 and x = 4.

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