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Simplifying 0 = 2x2 + -240x + 4800 Reorder the terms: 0 = 4800 + -240x + 2x2 Solving 0 = 4800 + -240x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -4800 = -4800 -4800 + 240x + -2x2 = 4800 + -240x + 2x2 + -4800 + 240x + -2x2 Reorder the terms: -4800 + 240x + -2x2 = 4800 + -4800 + -240x + 240x + 2x2 + -2x2 Combine like terms: 4800 + -4800 = 0 -4800 + 240x + -2x2 = 0 + -240x + 240x + 2x2 + -2x2 -4800 + 240x + -2x2 = -240x + 240x + 2x2 + -2x2 Combine like terms: -240x + 240x = 0 -4800 + 240x + -2x2 = 0 + 2x2 + -2x2 -4800 + 240x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4800 + 240x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2400 + 120x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2400 + 120x + -1x2)' equal to zero and attempt to solve: Simplifying -2400 + 120x + -1x2 = 0 Solving -2400 + 120x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2400 + -120x + x2 = 0 Move the constant term to the right: Add '-2400' to each side of the equation. 2400 + -120x + -2400 + x2 = 0 + -2400 Reorder the terms: 2400 + -2400 + -120x + x2 = 0 + -2400 Combine like terms: 2400 + -2400 = 0 0 + -120x + x2 = 0 + -2400 -120x + x2 = 0 + -2400 Combine like terms: 0 + -2400 = -2400 -120x + x2 = -2400 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 = -2400 + 3600 Reorder the terms: 3600 + -120x + x2 = -2400 + 3600 Combine like terms: -2400 + 3600 = 1200 3600 + -120x + x2 = 1200 Factor a perfect square on the left side: (x + -60)(x + -60) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + -60) equal to 34.641016151 and -34.641016151.Subproblem 1
x + -60 = 34.641016151 Simplifying x + -60 = 34.641016151 Reorder the terms: -60 + x = 34.641016151 Solving -60 + x = 34.641016151 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 = 34.641016151 + 60 Combine like terms: -60 + 60 = 0 0 + x = 34.641016151 + 60 x = 34.641016151 + 60 Combine like terms: 34.641016151 + 60 = 94.641016151 x = 94.641016151 Simplifying x = 94.641016151Subproblem 2
x + -60 = -34.641016151 Simplifying x + -60 = -34.641016151 Reorder the terms: -60 + x = -34.641016151 Solving -60 + x = -34.641016151 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 = -34.641016151 + 60 Combine like terms: -60 + 60 = 0 0 + x = -34.641016151 + 60 x = -34.641016151 + 60 Combine like terms: -34.641016151 + 60 = 25.358983849 x = 25.358983849 Simplifying x = 25.358983849Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.641016151, 25.358983849}Solution
x = {94.641016151, 25.358983849}
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