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Simplifying x2 + 120x = 3500 Reorder the terms: 120x + x2 = 3500 Solving 120x + x2 = 3500 Solving for variable 'x'. Reorder the terms: -3500 + 120x + x2 = 3500 + -3500 Combine like terms: 3500 + -3500 = 0 -3500 + 120x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3500' to each side of the equation. -3500 + 120x + 3500 + x2 = 0 + 3500 Reorder the terms: -3500 + 3500 + 120x + x2 = 0 + 3500 Combine like terms: -3500 + 3500 = 0 0 + 120x + x2 = 0 + 3500 120x + x2 = 0 + 3500 Combine like terms: 0 + 3500 = 3500 120x + x2 = 3500 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 = 3500 + 3600 Reorder the terms: 3600 + 120x + x2 = 3500 + 3600 Combine like terms: 3500 + 3600 = 7100 3600 + 120x + x2 = 7100 Factor a perfect square on the left side: (x + 60)(x + 60) = 7100 Calculate the square root of the right side: 84.261497732 Break this problem into two subproblems by setting (x + 60) equal to 84.261497732 and -84.261497732.Subproblem 1
x + 60 = 84.261497732 Simplifying x + 60 = 84.261497732 Reorder the terms: 60 + x = 84.261497732 Solving 60 + x = 84.261497732 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 = 84.261497732 + -60 Combine like terms: 60 + -60 = 0 0 + x = 84.261497732 + -60 x = 84.261497732 + -60 Combine like terms: 84.261497732 + -60 = 24.261497732 x = 24.261497732 Simplifying x = 24.261497732Subproblem 2
x + 60 = -84.261497732 Simplifying x + 60 = -84.261497732 Reorder the terms: 60 + x = -84.261497732 Solving 60 + x = -84.261497732 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 = -84.261497732 + -60 Combine like terms: 60 + -60 = 0 0 + x = -84.261497732 + -60 x = -84.261497732 + -60 Combine like terms: -84.261497732 + -60 = -144.261497732 x = -144.261497732 Simplifying x = -144.261497732Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.261497732, -144.261497732}
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