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Simplifying 2r2 + -50r + -42 = 0 Reorder the terms: -42 + -50r + 2r2 = 0 Solving -42 + -50r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -25r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -25r + r2)' equal to zero and attempt to solve: Simplifying -21 + -25r + r2 = 0 Solving -21 + -25r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -25r + 21 + r2 = 0 + 21 Reorder the terms: -21 + 21 + -25r + r2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -25r + r2 = 0 + 21 -25r + r2 = 0 + 21 Combine like terms: 0 + 21 = 21 -25r + r2 = 21 The r term is -25r. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25r + 156.25 + r2 = 21 + 156.25 Reorder the terms: 156.25 + -25r + r2 = 21 + 156.25 Combine like terms: 21 + 156.25 = 177.25 156.25 + -25r + r2 = 177.25 Factor a perfect square on the left side: (r + -12.5)(r + -12.5) = 177.25 Calculate the square root of the right side: 13.313526956 Break this problem into two subproblems by setting (r + -12.5) equal to 13.313526956 and -13.313526956.Subproblem 1
r + -12.5 = 13.313526956 Simplifying r + -12.5 = 13.313526956 Reorder the terms: -12.5 + r = 13.313526956 Solving -12.5 + r = 13.313526956 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + r = 13.313526956 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + r = 13.313526956 + 12.5 r = 13.313526956 + 12.5 Combine like terms: 13.313526956 + 12.5 = 25.813526956 r = 25.813526956 Simplifying r = 25.813526956Subproblem 2
r + -12.5 = -13.313526956 Simplifying r + -12.5 = -13.313526956 Reorder the terms: -12.5 + r = -13.313526956 Solving -12.5 + r = -13.313526956 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + r = -13.313526956 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + r = -13.313526956 + 12.5 r = -13.313526956 + 12.5 Combine like terms: -13.313526956 + 12.5 = -0.813526956 r = -0.813526956 Simplifying r = -0.813526956Solution
The solution to the problem is based on the solutions from the subproblems. r = {25.813526956, -0.813526956}Solution
r = {25.813526956, -0.813526956}
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