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Simplifying -2730 = -28000r2 + -56000r Reorder the terms: -2730 = -56000r + -28000r2 Solving -2730 = -56000r + -28000r2 Solving for variable 'r'. Reorder the terms: -2730 + 56000r + 28000r2 = -56000r + 56000r + -28000r2 + 28000r2 Combine like terms: -56000r + 56000r = 0 -2730 + 56000r + 28000r2 = 0 + -28000r2 + 28000r2 -2730 + 56000r + 28000r2 = -28000r2 + 28000r2 Combine like terms: -28000r2 + 28000r2 = 0 -2730 + 56000r + 28000r2 = 0 Factor out the Greatest Common Factor (GCF), '70'. 70(-39 + 800r + 400r2) = 0 Ignore the factor 70.Subproblem 1
Set the factor '(-39 + 800r + 400r2)' equal to zero and attempt to solve: Simplifying -39 + 800r + 400r2 = 0 Solving -39 + 800r + 400r2 = 0 Begin completing the square. Divide all terms by 400 the coefficient of the squared term: Divide each side by '400'. -0.0975 + 2r + r2 = 0.00 Move the constant term to the right: Add '0.0975' to each side of the equation. -0.0975 + 2r + 0.0975 + r2 = 0.00 + 0.0975 Reorder the terms: -0.0975 + 0.0975 + 2r + r2 = 0.00 + 0.0975 Combine like terms: -0.0975 + 0.0975 = 0.0000 0.0000 + 2r + r2 = 0.00 + 0.0975 2r + r2 = 0.00 + 0.0975 Combine like terms: 0.00 + 0.0975 = 0.0975 2r + r2 = 0.0975 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 0.0975 + 1 Reorder the terms: 1 + 2r + r2 = 0.0975 + 1 Combine like terms: 0.0975 + 1 = 1.0975 1 + 2r + r2 = 1.0975 Factor a perfect square on the left side: (r + 1)(r + 1) = 1.0975 Calculate the square root of the right side: 1.047616342 Break this problem into two subproblems by setting (r + 1) equal to 1.047616342 and -1.047616342.Subproblem 1
r + 1 = 1.047616342 Simplifying r + 1 = 1.047616342 Reorder the terms: 1 + r = 1.047616342 Solving 1 + r = 1.047616342 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 1.047616342 + -1 Combine like terms: 1 + -1 = 0 0 + r = 1.047616342 + -1 r = 1.047616342 + -1 Combine like terms: 1.047616342 + -1 = 0.047616342 r = 0.047616342 Simplifying r = 0.047616342Subproblem 2
r + 1 = -1.047616342 Simplifying r + 1 = -1.047616342 Reorder the terms: 1 + r = -1.047616342 Solving 1 + r = -1.047616342 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -1.047616342 + -1 Combine like terms: 1 + -1 = 0 0 + r = -1.047616342 + -1 r = -1.047616342 + -1 Combine like terms: -1.047616342 + -1 = -2.047616342 r = -2.047616342 Simplifying r = -2.047616342Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.047616342, -2.047616342}Solution
r = {0.047616342, -2.047616342}
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