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Simplifying 2x2 + -12x + -540 = 0 Reorder the terms: -540 + -12x + 2x2 = 0 Solving -540 + -12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-270 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-270 + -6x + x2)' equal to zero and attempt to solve: Simplifying -270 + -6x + x2 = 0 Solving -270 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + -6x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + -6x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -6x + x2 = 0 + 270 -6x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 -6x + x2 = 270 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 270 + 9 Reorder the terms: 9 + -6x + x2 = 270 + 9 Combine like terms: 270 + 9 = 279 9 + -6x + x2 = 279 Factor a perfect square on the left side: (x + -3)(x + -3) = 279 Calculate the square root of the right side: 16.703293088 Break this problem into two subproblems by setting (x + -3) equal to 16.703293088 and -16.703293088.Subproblem 1
x + -3 = 16.703293088 Simplifying x + -3 = 16.703293088 Reorder the terms: -3 + x = 16.703293088 Solving -3 + x = 16.703293088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 16.703293088 + 3 Combine like terms: -3 + 3 = 0 0 + x = 16.703293088 + 3 x = 16.703293088 + 3 Combine like terms: 16.703293088 + 3 = 19.703293088 x = 19.703293088 Simplifying x = 19.703293088Subproblem 2
x + -3 = -16.703293088 Simplifying x + -3 = -16.703293088 Reorder the terms: -3 + x = -16.703293088 Solving -3 + x = -16.703293088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -16.703293088 + 3 Combine like terms: -3 + 3 = 0 0 + x = -16.703293088 + 3 x = -16.703293088 + 3 Combine like terms: -16.703293088 + 3 = -13.703293088 x = -13.703293088 Simplifying x = -13.703293088Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.703293088, -13.703293088}Solution
x = {19.703293088, -13.703293088}
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