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Simplifying r2 + -15r = -8 + -10 Reorder the terms: -15r + r2 = -8 + -10 Combine like terms: -8 + -10 = -18 -15r + r2 = -18 Solving -15r + r2 = -18 Solving for variable 'r'. Reorder the terms: 18 + -15r + r2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + -15r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -15r + -18 + r2 = 0 + -18 Reorder the terms: 18 + -18 + -15r + r2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -15r + r2 = 0 + -18 -15r + r2 = 0 + -18 Combine like terms: 0 + -18 = -18 -15r + r2 = -18 The r term is -15r. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15r + 56.25 + r2 = -18 + 56.25 Reorder the terms: 56.25 + -15r + r2 = -18 + 56.25 Combine like terms: -18 + 56.25 = 38.25 56.25 + -15r + r2 = 38.25 Factor a perfect square on the left side: (r + -7.5)(r + -7.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (r + -7.5) equal to 6.184658438 and -6.184658438.Subproblem 1
r + -7.5 = 6.184658438 Simplifying r + -7.5 = 6.184658438 Reorder the terms: -7.5 + r = 6.184658438 Solving -7.5 + r = 6.184658438 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + r = 6.184658438 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + r = 6.184658438 + 7.5 r = 6.184658438 + 7.5 Combine like terms: 6.184658438 + 7.5 = 13.684658438 r = 13.684658438 Simplifying r = 13.684658438Subproblem 2
r + -7.5 = -6.184658438 Simplifying r + -7.5 = -6.184658438 Reorder the terms: -7.5 + r = -6.184658438 Solving -7.5 + r = -6.184658438 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + r = -6.184658438 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + r = -6.184658438 + 7.5 r = -6.184658438 + 7.5 Combine like terms: -6.184658438 + 7.5 = 1.315341562 r = 1.315341562 Simplifying r = 1.315341562Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.684658438, 1.315341562}
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