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Simplifying 5r2 + -55r + 15 = 0 Reorder the terms: 15 + -55r + 5r2 = 0 Solving 15 + -55r + 5r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -11r + r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -11r + r2)' equal to zero and attempt to solve: Simplifying 3 + -11r + r2 = 0 Solving 3 + -11r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + -11r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11r + r2 = 0 + -3 -11r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11r + r2 = -3 The r term is -11r. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11r + 30.25 + r2 = -3 + 30.25 Reorder the terms: 30.25 + -11r + r2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + -11r + r2 = 27.25 Factor a perfect square on the left side: (r + -5.5)(r + -5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (r + -5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
r + -5.5 = 5.220153254 Simplifying r + -5.5 = 5.220153254 Reorder the terms: -5.5 + r = 5.220153254 Solving -5.5 + r = 5.220153254 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = 5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = 5.220153254 + 5.5 r = 5.220153254 + 5.5 Combine like terms: 5.220153254 + 5.5 = 10.720153254 r = 10.720153254 Simplifying r = 10.720153254Subproblem 2
r + -5.5 = -5.220153254 Simplifying r + -5.5 = -5.220153254 Reorder the terms: -5.5 + r = -5.220153254 Solving -5.5 + r = -5.220153254 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = -5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = -5.220153254 + 5.5 r = -5.220153254 + 5.5 Combine like terms: -5.220153254 + 5.5 = 0.279846746 r = 0.279846746 Simplifying r = 0.279846746Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.720153254, 0.279846746}Solution
r = {10.720153254, 0.279846746}
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