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Simplifying 2x2 + -6x + -1080 = 0 Reorder the terms: -1080 + -6x + 2x2 = 0 Solving -1080 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-540 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-540 + -3x + x2)' equal to zero and attempt to solve: Simplifying -540 + -3x + x2 = 0 Solving -540 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + -3x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + -3x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + -3x + x2 = 0 + 540 -3x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 -3x + x2 = 540 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 540 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 540 + 2.25 Combine like terms: 540 + 2.25 = 542.25 2.25 + -3x + x2 = 542.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 542.25 Calculate the square root of the right side: 23.286262044 Break this problem into two subproblems by setting (x + -1.5) equal to 23.286262044 and -23.286262044.Subproblem 1
x + -1.5 = 23.286262044 Simplifying x + -1.5 = 23.286262044 Reorder the terms: -1.5 + x = 23.286262044 Solving -1.5 + x = 23.286262044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 23.286262044 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 23.286262044 + 1.5 x = 23.286262044 + 1.5 Combine like terms: 23.286262044 + 1.5 = 24.786262044 x = 24.786262044 Simplifying x = 24.786262044Subproblem 2
x + -1.5 = -23.286262044 Simplifying x + -1.5 = -23.286262044 Reorder the terms: -1.5 + x = -23.286262044 Solving -1.5 + x = -23.286262044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -23.286262044 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -23.286262044 + 1.5 x = -23.286262044 + 1.5 Combine like terms: -23.286262044 + 1.5 = -21.786262044 x = -21.786262044 Simplifying x = -21.786262044Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.786262044, -21.786262044}Solution
x = {24.786262044, -21.786262044}
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