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Simplifying 3x2 = 132x + 180 Reorder the terms: 3x2 = 180 + 132x Solving 3x2 = 180 + 132x Solving for variable 'x'. Reorder the terms: -180 + -132x + 3x2 = 180 + 132x + -180 + -132x Reorder the terms: -180 + -132x + 3x2 = 180 + -180 + 132x + -132x Combine like terms: 180 + -180 = 0 -180 + -132x + 3x2 = 0 + 132x + -132x -180 + -132x + 3x2 = 132x + -132x Combine like terms: 132x + -132x = 0 -180 + -132x + 3x2 = 0 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 = 544 484 + -44x + x2 = 544 Factor a perfect square on the left side: (x + -22)(x + -22) = 544 Calculate the square root of the right side: 23.323807579 Break this problem into two subproblems by setting (x + -22) equal to 23.323807579 and -23.323807579.Subproblem 1
x + -22 = 23.323807579 Simplifying x + -22 = 23.323807579 Reorder the terms: -22 + x = 23.323807579 Solving -22 + x = 23.323807579 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 = 23.323807579 + 22 Combine like terms: -22 + 22 = 0 0 + x = 23.323807579 + 22 x = 23.323807579 + 22 Combine like terms: 23.323807579 + 22 = 45.323807579 x = 45.323807579 Simplifying x = 45.323807579Subproblem 2
x + -22 = -23.323807579 Simplifying x + -22 = -23.323807579 Reorder the terms: -22 + x = -23.323807579 Solving -22 + x = -23.323807579 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 = -23.323807579 + 22 Combine like terms: -22 + 22 = 0 0 + x = -23.323807579 + 22 x = -23.323807579 + 22 Combine like terms: -23.323807579 + 22 = -1.323807579 x = -1.323807579 Simplifying x = -1.323807579Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.323807579, -1.323807579}Solution
x = {45.323807579, -1.323807579}
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