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Simplifying x2 + -120x + -3600 = 0 Reorder the terms: -3600 + -120x + x2 = 0 Solving -3600 + -120x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + -120x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + -120x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + -120x + x2 = 0 + 3600 -120x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 -120x + x2 = 3600 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 = 3600 + 3600 Reorder the terms: 3600 + -120x + x2 = 3600 + 3600 Combine like terms: 3600 + 3600 = 7200 3600 + -120x + x2 = 7200 Factor a perfect square on the left side: (x + -60)(x + -60) = 7200 Calculate the square root of the right side: 84.852813742 Break this problem into two subproblems by setting (x + -60) equal to 84.852813742 and -84.852813742.Subproblem 1
x + -60 = 84.852813742 Simplifying x + -60 = 84.852813742 Reorder the terms: -60 + x = 84.852813742 Solving -60 + x = 84.852813742 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 = 84.852813742 + 60 Combine like terms: -60 + 60 = 0 0 + x = 84.852813742 + 60 x = 84.852813742 + 60 Combine like terms: 84.852813742 + 60 = 144.852813742 x = 144.852813742 Simplifying x = 144.852813742Subproblem 2
x + -60 = -84.852813742 Simplifying x + -60 = -84.852813742 Reorder the terms: -60 + x = -84.852813742 Solving -60 + x = -84.852813742 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 = -84.852813742 + 60 Combine like terms: -60 + 60 = 0 0 + x = -84.852813742 + 60 x = -84.852813742 + 60 Combine like terms: -84.852813742 + 60 = -24.852813742 x = -24.852813742 Simplifying x = -24.852813742Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.852813742, -24.852813742}
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