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Simplifying 2r2 + -32r = 2 Reorder the terms: -32r + 2r2 = 2 Solving -32r + 2r2 = 2 Solving for variable 'r'. Reorder the terms: -2 + -32r + 2r2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -32r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -16r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -16r + r2)' equal to zero and attempt to solve: Simplifying -1 + -16r + r2 = 0 Solving -1 + -16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -16r + 1 + r2 = 0 + 1 Reorder the terms: -1 + 1 + -16r + r2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -16r + r2 = 0 + 1 -16r + r2 = 0 + 1 Combine like terms: 0 + 1 = 1 -16r + r2 = 1 The r term is -16r. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16r + 64 + r2 = 1 + 64 Reorder the terms: 64 + -16r + r2 = 1 + 64 Combine like terms: 1 + 64 = 65 64 + -16r + r2 = 65 Factor a perfect square on the left side: (r + -8)(r + -8) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (r + -8) equal to 8.062257748 and -8.062257748.Subproblem 1
r + -8 = 8.062257748 Simplifying r + -8 = 8.062257748 Reorder the terms: -8 + r = 8.062257748 Solving -8 + r = 8.062257748 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 8.062257748 + 8 Combine like terms: -8 + 8 = 0 0 + r = 8.062257748 + 8 r = 8.062257748 + 8 Combine like terms: 8.062257748 + 8 = 16.062257748 r = 16.062257748 Simplifying r = 16.062257748Subproblem 2
r + -8 = -8.062257748 Simplifying r + -8 = -8.062257748 Reorder the terms: -8 + r = -8.062257748 Solving -8 + r = -8.062257748 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = -8.062257748 + 8 Combine like terms: -8 + 8 = 0 0 + r = -8.062257748 + 8 r = -8.062257748 + 8 Combine like terms: -8.062257748 + 8 = -0.062257748 r = -0.062257748 Simplifying r = -0.062257748Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.062257748, -0.062257748}Solution
r = {16.062257748, -0.062257748}
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