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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 = 3100 3600 + 120x + x2 = 3100 Factor a perfect square on the left side: (x + 60)(x + 60) = 3100 Calculate the square root of the right side: 55.677643628 Break this problem into two subproblems by setting (x + 60) equal to 55.677643628 and -55.677643628.Subproblem 1
x + 60 = 55.677643628 Simplifying x + 60 = 55.677643628 Reorder the terms: 60 + x = 55.677643628 Solving 60 + x = 55.677643628 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 = 55.677643628 + -60 Combine like terms: 60 + -60 = 0 0 + x = 55.677643628 + -60 x = 55.677643628 + -60 Combine like terms: 55.677643628 + -60 = -4.322356372 x = -4.322356372 Simplifying x = -4.322356372Subproblem 2
x + 60 = -55.677643628 Simplifying x + 60 = -55.677643628 Reorder the terms: 60 + x = -55.677643628 Solving 60 + x = -55.677643628 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 = -55.677643628 + -60 Combine like terms: 60 + -60 = 0 0 + x = -55.677643628 + -60 x = -55.677643628 + -60 Combine like terms: -55.677643628 + -60 = -115.677643628 x = -115.677643628 Simplifying x = -115.677643628Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.322356372, -115.677643628}
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