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Simplifying 2r2 + -44r = -38 Reorder the terms: -44r + 2r2 = -38 Solving -44r + 2r2 = -38 Solving for variable 'r'. Reorder the terms: 38 + -44r + 2r2 = -38 + 38 Combine like terms: -38 + 38 = 0 38 + -44r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -22r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -22r + r2)' equal to zero and attempt to solve: Simplifying 19 + -22r + r2 = 0 Solving 19 + -22r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -22r + -19 + r2 = 0 + -19 Reorder the terms: 19 + -19 + -22r + r2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -22r + r2 = 0 + -19 -22r + r2 = 0 + -19 Combine like terms: 0 + -19 = -19 -22r + r2 = -19 The r term is -22r. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22r + 121 + r2 = -19 + 121 Reorder the terms: 121 + -22r + r2 = -19 + 121 Combine like terms: -19 + 121 = 102 121 + -22r + r2 = 102 Factor a perfect square on the left side: (r + -11)(r + -11) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (r + -11) equal to 10.099504938 and -10.099504938.Subproblem 1
r + -11 = 10.099504938 Simplifying r + -11 = 10.099504938 Reorder the terms: -11 + r = 10.099504938 Solving -11 + r = 10.099504938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + r = 10.099504938 + 11 Combine like terms: -11 + 11 = 0 0 + r = 10.099504938 + 11 r = 10.099504938 + 11 Combine like terms: 10.099504938 + 11 = 21.099504938 r = 21.099504938 Simplifying r = 21.099504938Subproblem 2
r + -11 = -10.099504938 Simplifying r + -11 = -10.099504938 Reorder the terms: -11 + r = -10.099504938 Solving -11 + r = -10.099504938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + r = -10.099504938 + 11 Combine like terms: -11 + 11 = 0 0 + r = -10.099504938 + 11 r = -10.099504938 + 11 Combine like terms: -10.099504938 + 11 = 0.900495062 r = 0.900495062 Simplifying r = 0.900495062Solution
The solution to the problem is based on the solutions from the subproblems. r = {21.099504938, 0.900495062}Solution
r = {21.099504938, 0.900495062}
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