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Simplifying 120 = 480x + -2x2 Solving 120 = 480x + -2x2 Solving for variable 'x'. Reorder the terms: 120 + -480x + 2x2 = 480x + -480x + -2x2 + 2x2 Combine like terms: 480x + -480x = 0 120 + -480x + 2x2 = 0 + -2x2 + 2x2 120 + -480x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 120 + -480x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -240x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -240x + x2)' equal to zero and attempt to solve: Simplifying 60 + -240x + x2 = 0 Solving 60 + -240x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -240x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -240x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -240x + x2 = 0 + -60 -240x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -240x + x2 = -60 The x term is -240x. Take half its coefficient (-120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. -240x + 14400 + x2 = -60 + 14400 Reorder the terms: 14400 + -240x + x2 = -60 + 14400 Combine like terms: -60 + 14400 = 14340 14400 + -240x + x2 = 14340 Factor a perfect square on the left side: (x + -120)(x + -120) = 14340 Calculate the square root of the right side: 119.749739039 Break this problem into two subproblems by setting (x + -120) equal to 119.749739039 and -119.749739039.Subproblem 1
x + -120 = 119.749739039 Simplifying x + -120 = 119.749739039 Reorder the terms: -120 + x = 119.749739039 Solving -120 + x = 119.749739039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = 119.749739039 + 120 Combine like terms: -120 + 120 = 0 0 + x = 119.749739039 + 120 x = 119.749739039 + 120 Combine like terms: 119.749739039 + 120 = 239.749739039 x = 239.749739039 Simplifying x = 239.749739039Subproblem 2
x + -120 = -119.749739039 Simplifying x + -120 = -119.749739039 Reorder the terms: -120 + x = -119.749739039 Solving -120 + x = -119.749739039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = -119.749739039 + 120 Combine like terms: -120 + 120 = 0 0 + x = -119.749739039 + 120 x = -119.749739039 + 120 Combine like terms: -119.749739039 + 120 = 0.250260961 x = 0.250260961 Simplifying x = 0.250260961Solution
The solution to the problem is based on the solutions from the subproblems. x = {239.749739039, 0.250260961}Solution
x = {239.749739039, 0.250260961}
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