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Simplifying 2r2 + 12r + -12 = 0 Reorder the terms: -12 + 12r + 2r2 = 0 Solving -12 + 12r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 6r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 6r + r2)' equal to zero and attempt to solve: Simplifying -6 + 6r + r2 = 0 Solving -6 + 6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 6r + 6 + r2 = 0 + 6 Reorder the terms: -6 + 6 + 6r + r2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6r + r2 = 0 + 6 6r + r2 = 0 + 6 Combine like terms: 0 + 6 = 6 6r + r2 = 6 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 = 6 + 9 Reorder the terms: 9 + 6r + r2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + 6r + r2 = 15 Factor a perfect square on the left side: (r + 3)(r + 3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (r + 3) equal to 3.872983346 and -3.872983346.Subproblem 1
r + 3 = 3.872983346 Simplifying r + 3 = 3.872983346 Reorder the terms: 3 + r = 3.872983346 Solving 3 + r = 3.872983346 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 = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + r = 3.872983346 + -3 r = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 r = 0.872983346 Simplifying r = 0.872983346Subproblem 2
r + 3 = -3.872983346 Simplifying r + 3 = -3.872983346 Reorder the terms: 3 + r = -3.872983346 Solving 3 + r = -3.872983346 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 = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + r = -3.872983346 + -3 r = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 r = -6.872983346 Simplifying r = -6.872983346Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.872983346, -6.872983346}Solution
r = {0.872983346, -6.872983346}
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