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Solve for r: (r-6)^2 + (r-3)^2 = r^2
Published on September 8, 2024
Algebra
Solve the equation (r-6)^2 + (r-3)^2 = r^2. The solution involves expanding the squares, combining like terms, and solving the resulting quadratic equation. The solutions are r = 15 and r = 3.
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:
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The left side of the equation has two squared terms:
and . Remember that squaring a binomial means multiplying it by itself: -
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Now, let’s expand these using the FOIL (First, Outer, Inner, Last) method:
-
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Substitute these expanded forms back into the original equation:
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(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:
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We can solve this by factoring:
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Set each factor equal to zero and solve for r:
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or -
or
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Therefore, the solutions to the equation are r = 15 and r = 3.