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Simplifying 2r2 + 14r = 144 Reorder the terms: 14r + 2r2 = 144 Solving 14r + 2r2 = 144 Solving for variable 'r'. Reorder the terms: -144 + 14r + 2r2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 14r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 7r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + 7r + r2)' equal to zero and attempt to solve: Simplifying -72 + 7r + r2 = 0 Solving -72 + 7r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 7r + 72 + r2 = 0 + 72 Reorder the terms: -72 + 72 + 7r + r2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 7r + r2 = 0 + 72 7r + r2 = 0 + 72 Combine like terms: 0 + 72 = 72 7r + r2 = 72 The r term is 7r. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7r + 12.25 + r2 = 72 + 12.25 Reorder the terms: 12.25 + 7r + r2 = 72 + 12.25 Combine like terms: 72 + 12.25 = 84.25 12.25 + 7r + r2 = 84.25 Factor a perfect square on the left side: (r + 3.5)(r + 3.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (r + 3.5) equal to 9.178779875 and -9.178779875.Subproblem 1
r + 3.5 = 9.178779875 Simplifying r + 3.5 = 9.178779875 Reorder the terms: 3.5 + r = 9.178779875 Solving 3.5 + r = 9.178779875 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + r = 9.178779875 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = 9.178779875 + -3.5 r = 9.178779875 + -3.5 Combine like terms: 9.178779875 + -3.5 = 5.678779875 r = 5.678779875 Simplifying r = 5.678779875Subproblem 2
r + 3.5 = -9.178779875 Simplifying r + 3.5 = -9.178779875 Reorder the terms: 3.5 + r = -9.178779875 Solving 3.5 + r = -9.178779875 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + r = -9.178779875 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + r = -9.178779875 + -3.5 r = -9.178779875 + -3.5 Combine like terms: -9.178779875 + -3.5 = -12.678779875 r = -12.678779875 Simplifying r = -12.678779875Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.678779875, -12.678779875}Solution
r = {5.678779875, -12.678779875}
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