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Simplifying -500 = 120x + -1x2 Solving -500 = 120x + -1x2 Solving for variable 'x'. Reorder the terms: -500 + -120x + x2 = 120x + -120x + -1x2 + x2 Combine like terms: 120x + -120x = 0 -500 + -120x + x2 = 0 + -1x2 + x2 -500 + -120x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -500 + -120x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -120x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -120x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -120x + x2 = 0 + 500 -120x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -120x + x2 = 500 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 = 500 + 3600 Reorder the terms: 3600 + -120x + x2 = 500 + 3600 Combine like terms: 500 + 3600 = 4100 3600 + -120x + x2 = 4100 Factor a perfect square on the left side: (x + -60)(x + -60) = 4100 Calculate the square root of the right side: 64.031242374 Break this problem into two subproblems by setting (x + -60) equal to 64.031242374 and -64.031242374.Subproblem 1
x + -60 = 64.031242374 Simplifying x + -60 = 64.031242374 Reorder the terms: -60 + x = 64.031242374 Solving -60 + x = 64.031242374 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 = 64.031242374 + 60 Combine like terms: -60 + 60 = 0 0 + x = 64.031242374 + 60 x = 64.031242374 + 60 Combine like terms: 64.031242374 + 60 = 124.031242374 x = 124.031242374 Simplifying x = 124.031242374Subproblem 2
x + -60 = -64.031242374 Simplifying x + -60 = -64.031242374 Reorder the terms: -60 + x = -64.031242374 Solving -60 + x = -64.031242374 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 = -64.031242374 + 60 Combine like terms: -60 + 60 = 0 0 + x = -64.031242374 + 60 x = -64.031242374 + 60 Combine like terms: -64.031242374 + 60 = -4.031242374 x = -4.031242374 Simplifying x = -4.031242374Solution
The solution to the problem is based on the solutions from the subproblems. x = {124.031242374, -4.031242374}
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