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Simplifying r2 + -10r + (-5) = -17 r2 + -10r + -5 = -17 Reorder the terms: -5 + -10r + r2 = -17 Solving -5 + -10r + r2 = -17 Solving for variable 'r'. Reorder the terms: -5 + 17 + -10r + r2 = -17 + 17 Combine like terms: -5 + 17 = 12 12 + -10r + r2 = -17 + 17 Combine like terms: -17 + 17 = 0 12 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -10r + -12 + r2 = 0 + -12 Reorder the terms: 12 + -12 + -10r + r2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -10r + r2 = 0 + -12 -10r + r2 = 0 + -12 Combine like terms: 0 + -12 = -12 -10r + r2 = -12 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 = -12 + 25 Reorder the terms: 25 + -10r + r2 = -12 + 25 Combine like terms: -12 + 25 = 13 25 + -10r + r2 = 13 Factor a perfect square on the left side: (r + -5)(r + -5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (r + -5) equal to 3.605551275 and -3.605551275.Subproblem 1
r + -5 = 3.605551275 Simplifying r + -5 = 3.605551275 Reorder the terms: -5 + r = 3.605551275 Solving -5 + r = 3.605551275 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 = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + r = 3.605551275 + 5 r = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 r = 8.605551275 Simplifying r = 8.605551275Subproblem 2
r + -5 = -3.605551275 Simplifying r + -5 = -3.605551275 Reorder the terms: -5 + r = -3.605551275 Solving -5 + r = -3.605551275 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 = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + r = -3.605551275 + 5 r = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 r = 1.394448725 Simplifying r = 1.394448725Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.605551275, 1.394448725}
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