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Simplifying 100r2 + -850r + -40000 = 0 Reorder the terms: -40000 + -850r + 100r2 = 0 Solving -40000 + -850r + 100r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '50'. 50(-800 + -17r + 2r2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-800 + -17r + 2r2)' equal to zero and attempt to solve: Simplifying -800 + -17r + 2r2 = 0 Solving -800 + -17r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -400 + -8.5r + r2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -8.5r + 400 + r2 = 0 + 400 Reorder the terms: -400 + 400 + -8.5r + r2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -8.5r + r2 = 0 + 400 -8.5r + r2 = 0 + 400 Combine like terms: 0 + 400 = 400 -8.5r + r2 = 400 The r term is -8.5r. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5r + 18.0625 + r2 = 400 + 18.0625 Reorder the terms: 18.0625 + -8.5r + r2 = 400 + 18.0625 Combine like terms: 400 + 18.0625 = 418.0625 18.0625 + -8.5r + r2 = 418.0625 Factor a perfect square on the left side: (r + -4.25)(r + -4.25) = 418.0625 Calculate the square root of the right side: 20.446576731 Break this problem into two subproblems by setting (r + -4.25) equal to 20.446576731 and -20.446576731.Subproblem 1
r + -4.25 = 20.446576731 Simplifying r + -4.25 = 20.446576731 Reorder the terms: -4.25 + r = 20.446576731 Solving -4.25 + r = 20.446576731 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + r = 20.446576731 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + r = 20.446576731 + 4.25 r = 20.446576731 + 4.25 Combine like terms: 20.446576731 + 4.25 = 24.696576731 r = 24.696576731 Simplifying r = 24.696576731Subproblem 2
r + -4.25 = -20.446576731 Simplifying r + -4.25 = -20.446576731 Reorder the terms: -4.25 + r = -20.446576731 Solving -4.25 + r = -20.446576731 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + r = -20.446576731 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + r = -20.446576731 + 4.25 r = -20.446576731 + 4.25 Combine like terms: -20.446576731 + 4.25 = -16.196576731 r = -16.196576731 Simplifying r = -16.196576731Solution
The solution to the problem is based on the solutions from the subproblems. r = {24.696576731, -16.196576731}Solution
r = {24.696576731, -16.196576731}
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