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Simplifying 2r2 + 4r + -202 = 0 Reorder the terms: -202 + 4r + 2r2 = 0 Solving -202 + 4r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-101 + 2r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-101 + 2r + r2)' equal to zero and attempt to solve: Simplifying -101 + 2r + r2 = 0 Solving -101 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + 2r + 101 + r2 = 0 + 101 Reorder the terms: -101 + 101 + 2r + r2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + 2r + r2 = 0 + 101 2r + r2 = 0 + 101 Combine like terms: 0 + 101 = 101 2r + r2 = 101 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 101 + 1 Reorder the terms: 1 + 2r + r2 = 101 + 1 Combine like terms: 101 + 1 = 102 1 + 2r + r2 = 102 Factor a perfect square on the left side: (r + 1)(r + 1) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (r + 1) equal to 10.099504938 and -10.099504938.Subproblem 1
r + 1 = 10.099504938 Simplifying r + 1 = 10.099504938 Reorder the terms: 1 + r = 10.099504938 Solving 1 + r = 10.099504938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 10.099504938 + -1 Combine like terms: 1 + -1 = 0 0 + r = 10.099504938 + -1 r = 10.099504938 + -1 Combine like terms: 10.099504938 + -1 = 9.099504938 r = 9.099504938 Simplifying r = 9.099504938Subproblem 2
r + 1 = -10.099504938 Simplifying r + 1 = -10.099504938 Reorder the terms: 1 + r = -10.099504938 Solving 1 + r = -10.099504938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -10.099504938 + -1 Combine like terms: 1 + -1 = 0 0 + r = -10.099504938 + -1 r = -10.099504938 + -1 Combine like terms: -10.099504938 + -1 = -11.099504938 r = -11.099504938 Simplifying r = -11.099504938Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.099504938, -11.099504938}Solution
r = {9.099504938, -11.099504938}
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