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Simplifying r2 + 20r + -80 = -5 Reorder the terms: -80 + 20r + r2 = -5 Solving -80 + 20r + r2 = -5 Solving for variable 'r'. Reorder the terms: -80 + 5 + 20r + r2 = -5 + 5 Combine like terms: -80 + 5 = -75 -75 + 20r + r2 = -5 + 5 Combine like terms: -5 + 5 = 0 -75 + 20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 20r + 75 + r2 = 0 + 75 Reorder the terms: -75 + 75 + 20r + r2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 20r + r2 = 0 + 75 20r + r2 = 0 + 75 Combine like terms: 0 + 75 = 75 20r + r2 = 75 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 = 75 + 100 Reorder the terms: 100 + 20r + r2 = 75 + 100 Combine like terms: 75 + 100 = 175 100 + 20r + r2 = 175 Factor a perfect square on the left side: (r + 10)(r + 10) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (r + 10) equal to 13.228756555 and -13.228756555.Subproblem 1
r + 10 = 13.228756555 Simplifying r + 10 = 13.228756555 Reorder the terms: 10 + r = 13.228756555 Solving 10 + r = 13.228756555 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 = 13.228756555 + -10 Combine like terms: 10 + -10 = 0 0 + r = 13.228756555 + -10 r = 13.228756555 + -10 Combine like terms: 13.228756555 + -10 = 3.228756555 r = 3.228756555 Simplifying r = 3.228756555Subproblem 2
r + 10 = -13.228756555 Simplifying r + 10 = -13.228756555 Reorder the terms: 10 + r = -13.228756555 Solving 10 + r = -13.228756555 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 = -13.228756555 + -10 Combine like terms: 10 + -10 = 0 0 + r = -13.228756555 + -10 r = -13.228756555 + -10 Combine like terms: -13.228756555 + -10 = -23.228756555 r = -23.228756555 Simplifying r = -23.228756555Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.228756555, -23.228756555}
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