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Simplifying r2 + -2100r + 100000 = 0 Reorder the terms: 100000 + -2100r + r2 = 0 Solving 100000 + -2100r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-100000' to each side of the equation. 100000 + -2100r + -100000 + r2 = 0 + -100000 Reorder the terms: 100000 + -100000 + -2100r + r2 = 0 + -100000 Combine like terms: 100000 + -100000 = 0 0 + -2100r + r2 = 0 + -100000 -2100r + r2 = 0 + -100000 Combine like terms: 0 + -100000 = -100000 -2100r + r2 = -100000 The r term is -2100r. Take half its coefficient (-1050). Square it (1102500) and add it to both sides. Add '1102500' to each side of the equation. -2100r + 1102500 + r2 = -100000 + 1102500 Reorder the terms: 1102500 + -2100r + r2 = -100000 + 1102500 Combine like terms: -100000 + 1102500 = 1002500 1102500 + -2100r + r2 = 1002500 Factor a perfect square on the left side: (r + -1050)(r + -1050) = 1002500 Calculate the square root of the right side: 1001.249219725 Break this problem into two subproblems by setting (r + -1050) equal to 1001.249219725 and -1001.249219725.Subproblem 1
r + -1050 = 1001.249219725 Simplifying r + -1050 = 1001.249219725 Reorder the terms: -1050 + r = 1001.249219725 Solving -1050 + r = 1001.249219725 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1050' to each side of the equation. -1050 + 1050 + r = 1001.249219725 + 1050 Combine like terms: -1050 + 1050 = 0 0 + r = 1001.249219725 + 1050 r = 1001.249219725 + 1050 Combine like terms: 1001.249219725 + 1050 = 2051.249219725 r = 2051.249219725 Simplifying r = 2051.249219725Subproblem 2
r + -1050 = -1001.249219725 Simplifying r + -1050 = -1001.249219725 Reorder the terms: -1050 + r = -1001.249219725 Solving -1050 + r = -1001.249219725 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1050' to each side of the equation. -1050 + 1050 + r = -1001.249219725 + 1050 Combine like terms: -1050 + 1050 = 0 0 + r = -1001.249219725 + 1050 r = -1001.249219725 + 1050 Combine like terms: -1001.249219725 + 1050 = 48.750780275 r = 48.750780275 Simplifying r = 48.750780275Solution
The solution to the problem is based on the solutions from the subproblems. r = {2051.249219725, 48.750780275}
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