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Simplifying x2 + -120x = -2780 Reorder the terms: -120x + x2 = -2780 Solving -120x + x2 = -2780 Solving for variable 'x'. Reorder the terms: 2780 + -120x + x2 = -2780 + 2780 Combine like terms: -2780 + 2780 = 0 2780 + -120x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2780' to each side of the equation. 2780 + -120x + -2780 + x2 = 0 + -2780 Reorder the terms: 2780 + -2780 + -120x + x2 = 0 + -2780 Combine like terms: 2780 + -2780 = 0 0 + -120x + x2 = 0 + -2780 -120x + x2 = 0 + -2780 Combine like terms: 0 + -2780 = -2780 -120x + x2 = -2780 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 = -2780 + 3600 Reorder the terms: 3600 + -120x + x2 = -2780 + 3600 Combine like terms: -2780 + 3600 = 820 3600 + -120x + x2 = 820 Factor a perfect square on the left side: (x + -60)(x + -60) = 820 Calculate the square root of the right side: 28.635642127 Break this problem into two subproblems by setting (x + -60) equal to 28.635642127 and -28.635642127.Subproblem 1
x + -60 = 28.635642127 Simplifying x + -60 = 28.635642127 Reorder the terms: -60 + x = 28.635642127 Solving -60 + x = 28.635642127 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 = 28.635642127 + 60 Combine like terms: -60 + 60 = 0 0 + x = 28.635642127 + 60 x = 28.635642127 + 60 Combine like terms: 28.635642127 + 60 = 88.635642127 x = 88.635642127 Simplifying x = 88.635642127Subproblem 2
x + -60 = -28.635642127 Simplifying x + -60 = -28.635642127 Reorder the terms: -60 + x = -28.635642127 Solving -60 + x = -28.635642127 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 = -28.635642127 + 60 Combine like terms: -60 + 60 = 0 0 + x = -28.635642127 + 60 x = -28.635642127 + 60 Combine like terms: -28.635642127 + 60 = 31.364357873 x = 31.364357873 Simplifying x = 31.364357873Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.635642127, 31.364357873}
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