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Simplifying 3x2 + 132x + 180 = 0 Reorder the terms: 180 + 132x + 3x2 = 0 Solving 180 + 132x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(60 + 44x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(60 + 44x + x2)' equal to zero and attempt to solve: Simplifying 60 + 44x + x2 = 0 Solving 60 + 44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 44x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 44x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 44x + x2 = 0 + -60 44x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 44x + x2 = -60 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = -60 + 484 Reorder the terms: 484 + 44x + x2 = -60 + 484 Combine like terms: -60 + 484 = 424 484 + 44x + x2 = 424 Factor a perfect square on the left side: (x + 22)(x + 22) = 424 Calculate the square root of the right side: 20.591260282 Break this problem into two subproblems by setting (x + 22) equal to 20.591260282 and -20.591260282.Subproblem 1
x + 22 = 20.591260282 Simplifying x + 22 = 20.591260282 Reorder the terms: 22 + x = 20.591260282 Solving 22 + x = 20.591260282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 20.591260282 + -22 Combine like terms: 22 + -22 = 0 0 + x = 20.591260282 + -22 x = 20.591260282 + -22 Combine like terms: 20.591260282 + -22 = -1.408739718 x = -1.408739718 Simplifying x = -1.408739718Subproblem 2
x + 22 = -20.591260282 Simplifying x + 22 = -20.591260282 Reorder the terms: 22 + x = -20.591260282 Solving 22 + x = -20.591260282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -20.591260282 + -22 Combine like terms: 22 + -22 = 0 0 + x = -20.591260282 + -22 x = -20.591260282 + -22 Combine like terms: -20.591260282 + -22 = -42.591260282 x = -42.591260282 Simplifying x = -42.591260282Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.408739718, -42.591260282}Solution
x = {-1.408739718, -42.591260282}
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