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Simplifying 3x2 + -102x + -180 = 0 Reorder the terms: -180 + -102x + 3x2 = 0 Solving -180 + -102x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + -34x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + -34x + x2)' equal to zero and attempt to solve: Simplifying -60 + -34x + x2 = 0 Solving -60 + -34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -34x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -34x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -34x + x2 = 0 + 60 -34x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -34x + x2 = 60 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 60 + 289 Reorder the terms: 289 + -34x + x2 = 60 + 289 Combine like terms: 60 + 289 = 349 289 + -34x + x2 = 349 Factor a perfect square on the left side: (x + -17)(x + -17) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (x + -17) equal to 18.681541692 and -18.681541692.Subproblem 1
x + -17 = 18.681541692 Simplifying x + -17 = 18.681541692 Reorder the terms: -17 + x = 18.681541692 Solving -17 + x = 18.681541692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 18.681541692 + 17 Combine like terms: -17 + 17 = 0 0 + x = 18.681541692 + 17 x = 18.681541692 + 17 Combine like terms: 18.681541692 + 17 = 35.681541692 x = 35.681541692 Simplifying x = 35.681541692Subproblem 2
x + -17 = -18.681541692 Simplifying x + -17 = -18.681541692 Reorder the terms: -17 + x = -18.681541692 Solving -17 + x = -18.681541692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -18.681541692 + 17 Combine like terms: -17 + 17 = 0 0 + x = -18.681541692 + 17 x = -18.681541692 + 17 Combine like terms: -18.681541692 + 17 = -1.681541692 x = -1.681541692 Simplifying x = -1.681541692Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.681541692, -1.681541692}Solution
x = {35.681541692, -1.681541692}
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