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Simplifying r2 + -10r + -99 = 0 Reorder the terms: -99 + -10r + r2 = 0 Solving -99 + -10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -10r + 99 + r2 = 0 + 99 Reorder the terms: -99 + 99 + -10r + r2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -10r + r2 = 0 + 99 -10r + r2 = 0 + 99 Combine like terms: 0 + 99 = 99 -10r + r2 = 99 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = 99 + 25 Reorder the terms: 25 + -10r + r2 = 99 + 25 Combine like terms: 99 + 25 = 124 25 + -10r + r2 = 124 Factor a perfect square on the left side: (r + -5)(r + -5) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (r + -5) equal to 11.135528726 and -11.135528726.Subproblem 1
r + -5 = 11.135528726 Simplifying r + -5 = 11.135528726 Reorder the terms: -5 + r = 11.135528726 Solving -5 + r = 11.135528726 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 11.135528726 + 5 Combine like terms: -5 + 5 = 0 0 + r = 11.135528726 + 5 r = 11.135528726 + 5 Combine like terms: 11.135528726 + 5 = 16.135528726 r = 16.135528726 Simplifying r = 16.135528726Subproblem 2
r + -5 = -11.135528726 Simplifying r + -5 = -11.135528726 Reorder the terms: -5 + r = -11.135528726 Solving -5 + r = -11.135528726 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -11.135528726 + 5 Combine like terms: -5 + 5 = 0 0 + r = -11.135528726 + 5 r = -11.135528726 + 5 Combine like terms: -11.135528726 + 5 = -6.135528726 r = -6.135528726 Simplifying r = -6.135528726Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.135528726, -6.135528726}
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