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Simplifying 0 = 2x2 + -240x + 5280 Reorder the terms: 0 = 5280 + -240x + 2x2 Solving 0 = 5280 + -240x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -5280 = -5280 -5280 + 240x + -2x2 = 5280 + -240x + 2x2 + -5280 + 240x + -2x2 Reorder the terms: -5280 + 240x + -2x2 = 5280 + -5280 + -240x + 240x + 2x2 + -2x2 Combine like terms: 5280 + -5280 = 0 -5280 + 240x + -2x2 = 0 + -240x + 240x + 2x2 + -2x2 -5280 + 240x + -2x2 = -240x + 240x + 2x2 + -2x2 Combine like terms: -240x + 240x = 0 -5280 + 240x + -2x2 = 0 + 2x2 + -2x2 -5280 + 240x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5280 + 240x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2640 + 120x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2640 + 120x + -1x2)' equal to zero and attempt to solve: Simplifying -2640 + 120x + -1x2 = 0 Solving -2640 + 120x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2640 + -120x + x2 = 0 Move the constant term to the right: Add '-2640' to each side of the equation. 2640 + -120x + -2640 + x2 = 0 + -2640 Reorder the terms: 2640 + -2640 + -120x + x2 = 0 + -2640 Combine like terms: 2640 + -2640 = 0 0 + -120x + x2 = 0 + -2640 -120x + x2 = 0 + -2640 Combine like terms: 0 + -2640 = -2640 -120x + x2 = -2640 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -2640 + 3600 Reorder the terms: 3600 + -120x + x2 = -2640 + 3600 Combine like terms: -2640 + 3600 = 960 3600 + -120x + x2 = 960 Factor a perfect square on the left side: (x + -60)(x + -60) = 960 Calculate the square root of the right side: 30.98386677 Break this problem into two subproblems by setting (x + -60) equal to 30.98386677 and -30.98386677.Subproblem 1
x + -60 = 30.98386677 Simplifying x + -60 = 30.98386677 Reorder the terms: -60 + x = 30.98386677 Solving -60 + x = 30.98386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 30.98386677 + 60 Combine like terms: -60 + 60 = 0 0 + x = 30.98386677 + 60 x = 30.98386677 + 60 Combine like terms: 30.98386677 + 60 = 90.98386677 x = 90.98386677 Simplifying x = 90.98386677Subproblem 2
x + -60 = -30.98386677 Simplifying x + -60 = -30.98386677 Reorder the terms: -60 + x = -30.98386677 Solving -60 + x = -30.98386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -30.98386677 + 60 Combine like terms: -60 + 60 = 0 0 + x = -30.98386677 + 60 x = -30.98386677 + 60 Combine like terms: -30.98386677 + 60 = 29.01613323 x = 29.01613323 Simplifying x = 29.01613323Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.98386677, 29.01613323}Solution
x = {90.98386677, 29.01613323}
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