Solve for r: (r-6)^2 + (r-3)^2 = r^2

Published on September 8, 2024

Question

(r-6)^2 + (r-3)^2 = r^2 Solve it

Answer

Let’s break down this equation step-by-step.
(1) Expand the squares:
  • The left side of the equation has two squared terms: and . Remember that squaring a binomial means multiplying it by itself:
  • Now, let’s expand these using the FOIL (First, Outer, Inner, Last) method:
  • Substitute these expanded forms back into the original equation:
(2) Combine like terms:
  • Combine all the , , and constant terms on the left side:
(3) Move all terms to one side:
  • Subtract from both sides to get a quadratic equation:
(4) Solve the quadratic equation:
  • We can solve this by factoring:
  • Set each factor equal to zero and solve for r:
    • or
    • or
Therefore, the solutions to the equation are r = 15 and r = 3.
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