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Simplifying r2 + -20r = -65 Reorder the terms: -20r + r2 = -65 Solving -20r + r2 = -65 Solving for variable 'r'. Reorder the terms: 65 + -20r + r2 = -65 + 65 Combine like terms: -65 + 65 = 0 65 + -20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-65' to each side of the equation. 65 + -20r + -65 + r2 = 0 + -65 Reorder the terms: 65 + -65 + -20r + r2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -20r + r2 = 0 + -65 -20r + r2 = 0 + -65 Combine like terms: 0 + -65 = -65 -20r + r2 = -65 The r term is -20r. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20r + 100 + r2 = -65 + 100 Reorder the terms: 100 + -20r + r2 = -65 + 100 Combine like terms: -65 + 100 = 35 100 + -20r + r2 = 35 Factor a perfect square on the left side: (r + -10)(r + -10) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (r + -10) equal to 5.916079783 and -5.916079783.Subproblem 1
r + -10 = 5.916079783 Simplifying r + -10 = 5.916079783 Reorder the terms: -10 + r = 5.916079783 Solving -10 + r = 5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 5.916079783 + 10 Combine like terms: -10 + 10 = 0 0 + r = 5.916079783 + 10 r = 5.916079783 + 10 Combine like terms: 5.916079783 + 10 = 15.916079783 r = 15.916079783 Simplifying r = 15.916079783Subproblem 2
r + -10 = -5.916079783 Simplifying r + -10 = -5.916079783 Reorder the terms: -10 + r = -5.916079783 Solving -10 + r = -5.916079783 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -5.916079783 + 10 Combine like terms: -10 + 10 = 0 0 + r = -5.916079783 + 10 r = -5.916079783 + 10 Combine like terms: -5.916079783 + 10 = 4.083920217 r = 4.083920217 Simplifying r = 4.083920217Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.916079783, 4.083920217}
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