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Simplifying 5r2 + -20r + -9 = 6 Reorder the terms: -9 + -20r + 5r2 = 6 Solving -9 + -20r + 5r2 = 6 Solving for variable 'r'. Reorder the terms: -9 + -6 + -20r + 5r2 = 6 + -6 Combine like terms: -9 + -6 = -15 -15 + -20r + 5r2 = 6 + -6 Combine like terms: 6 + -6 = 0 -15 + -20r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + -4r + r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -4r + r2)' equal to zero and attempt to solve: Simplifying -3 + -4r + r2 = 0 Solving -3 + -4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -4r + 3 + r2 = 0 + 3 Reorder the terms: -3 + 3 + -4r + r2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4r + r2 = 0 + 3 -4r + r2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4r + r2 = 3 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 3 + 4 Reorder the terms: 4 + -4r + r2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4r + r2 = 7 Factor a perfect square on the left side: (r + -2)(r + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (r + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
r + -2 = 2.645751311 Simplifying r + -2 = 2.645751311 Reorder the terms: -2 + r = 2.645751311 Solving -2 + r = 2.645751311 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.645751311 + 2 r = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 r = 4.645751311 Simplifying r = 4.645751311Subproblem 2
r + -2 = -2.645751311 Simplifying r + -2 = -2.645751311 Reorder the terms: -2 + r = -2.645751311 Solving -2 + r = -2.645751311 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.645751311 + 2 r = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 r = -0.645751311 Simplifying r = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.645751311, -0.645751311}Solution
r = {4.645751311, -0.645751311}
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