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Simplifying r2 + -30r + -600 = 0 Reorder the terms: -600 + -30r + r2 = 0 Solving -600 + -30r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -30r + 600 + r2 = 0 + 600 Reorder the terms: -600 + 600 + -30r + r2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -30r + r2 = 0 + 600 -30r + r2 = 0 + 600 Combine like terms: 0 + 600 = 600 -30r + r2 = 600 The r term is -30r. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30r + 225 + r2 = 600 + 225 Reorder the terms: 225 + -30r + r2 = 600 + 225 Combine like terms: 600 + 225 = 825 225 + -30r + r2 = 825 Factor a perfect square on the left side: (r + -15)(r + -15) = 825 Calculate the square root of the right side: 28.722813233 Break this problem into two subproblems by setting (r + -15) equal to 28.722813233 and -28.722813233.Subproblem 1
r + -15 = 28.722813233 Simplifying r + -15 = 28.722813233 Reorder the terms: -15 + r = 28.722813233 Solving -15 + r = 28.722813233 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = 28.722813233 + 15 Combine like terms: -15 + 15 = 0 0 + r = 28.722813233 + 15 r = 28.722813233 + 15 Combine like terms: 28.722813233 + 15 = 43.722813233 r = 43.722813233 Simplifying r = 43.722813233Subproblem 2
r + -15 = -28.722813233 Simplifying r + -15 = -28.722813233 Reorder the terms: -15 + r = -28.722813233 Solving -15 + r = -28.722813233 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = -28.722813233 + 15 Combine like terms: -15 + 15 = 0 0 + r = -28.722813233 + 15 r = -28.722813233 + 15 Combine like terms: -28.722813233 + 15 = -13.722813233 r = -13.722813233 Simplifying r = -13.722813233Solution
The solution to the problem is based on the solutions from the subproblems. r = {43.722813233, -13.722813233}
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