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(x-8)^2-7=25 Square Root

less than a minute read Jun 17, 2024
(x-8)^2-7=25 Square Root

Solving the Equation: (x-8)² - 7 = 25

This equation involves a square term, so we'll need to use some algebraic manipulation to solve for x. Let's break it down step-by-step:

1. Isolate the Squared Term:

  • Add 7 to both sides of the equation: (x - 8)² = 32

2. Take the Square Root of Both Sides:

  • Remember that taking the square root introduces both positive and negative solutions. √(x - 8)² = ±√32

  • Simplify: x - 8 = ±√32

3. Simplify the Radical:

  • Find the prime factorization of 32: 32 = 2 x 2 x 2 x 2 x 2
  • Since we have a pair of 2s, we can take one 2 out of the radical: x - 8 = ±4√2

4. Isolate x:

  • Add 8 to both sides: x = 8 ± 4√2

Therefore, the solutions to the equation (x-8)² - 7 = 25 are:

  • x = 8 + 4√2
  • x = 8 - 4√2

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