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Simplifying r2 + -12r + -73 = 0 Reorder the terms: -73 + -12r + r2 = 0 Solving -73 + -12r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -12r + 73 + r2 = 0 + 73 Reorder the terms: -73 + 73 + -12r + r2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -12r + r2 = 0 + 73 -12r + r2 = 0 + 73 Combine like terms: 0 + 73 = 73 -12r + r2 = 73 The r term is -12r. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12r + 36 + r2 = 73 + 36 Reorder the terms: 36 + -12r + r2 = 73 + 36 Combine like terms: 73 + 36 = 109 36 + -12r + r2 = 109 Factor a perfect square on the left side: (r + -6)(r + -6) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (r + -6) equal to 10.440306509 and -10.440306509.Subproblem 1
r + -6 = 10.440306509 Simplifying r + -6 = 10.440306509 Reorder the terms: -6 + r = 10.440306509 Solving -6 + r = 10.440306509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = 10.440306509 + 6 Combine like terms: -6 + 6 = 0 0 + r = 10.440306509 + 6 r = 10.440306509 + 6 Combine like terms: 10.440306509 + 6 = 16.440306509 r = 16.440306509 Simplifying r = 16.440306509Subproblem 2
r + -6 = -10.440306509 Simplifying r + -6 = -10.440306509 Reorder the terms: -6 + r = -10.440306509 Solving -6 + r = -10.440306509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + r = -10.440306509 + 6 Combine like terms: -6 + 6 = 0 0 + r = -10.440306509 + 6 r = -10.440306509 + 6 Combine like terms: -10.440306509 + 6 = -4.440306509 r = -4.440306509 Simplifying r = -4.440306509Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.440306509, -4.440306509}
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