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Simplifying 2r2 + -12r + 6 = 0 Reorder the terms: 6 + -12r + 2r2 = 0 Solving 6 + -12r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -6r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -6r + r2)' equal to zero and attempt to solve: Simplifying 3 + -6r + r2 = 0 Solving 3 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6r + -3 + r2 = 0 + -3 Reorder the terms: 3 + -3 + -6r + r2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6r + r2 = 0 + -3 -6r + r2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6r + r2 = -3 The r term is -6r. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6r + 9 + r2 = -3 + 9 Reorder the terms: 9 + -6r + r2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6r + r2 = 6 Factor a perfect square on the left side: (r + -3)(r + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (r + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
r + -3 = 2.449489743 Simplifying r + -3 = 2.449489743 Reorder the terms: -3 + r = 2.449489743 Solving -3 + r = 2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + r = 2.449489743 + 3 r = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 r = 5.449489743 Simplifying r = 5.449489743Subproblem 2
r + -3 = -2.449489743 Simplifying r + -3 = -2.449489743 Reorder the terms: -3 + r = -2.449489743 Solving -3 + r = -2.449489743 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + r = -2.449489743 + 3 r = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 r = 0.550510257 Simplifying r = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.449489743, 0.550510257}Solution
r = {5.449489743, 0.550510257}
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