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Simplifying 120x + -1x2 = 11 Solving 120x + -1x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 120x + -1x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 120x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -120x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -120x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -120x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -120x + x2 = 0 + -11 -120x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -120x + x2 = -11 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 = -11 + 3600 Reorder the terms: 3600 + -120x + x2 = -11 + 3600 Combine like terms: -11 + 3600 = 3589 3600 + -120x + x2 = 3589 Factor a perfect square on the left side: (x + -60)(x + -60) = 3589 Calculate the square root of the right side: 59.908263203 Break this problem into two subproblems by setting (x + -60) equal to 59.908263203 and -59.908263203.Subproblem 1
x + -60 = 59.908263203 Simplifying x + -60 = 59.908263203 Reorder the terms: -60 + x = 59.908263203 Solving -60 + x = 59.908263203 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 = 59.908263203 + 60 Combine like terms: -60 + 60 = 0 0 + x = 59.908263203 + 60 x = 59.908263203 + 60 Combine like terms: 59.908263203 + 60 = 119.908263203 x = 119.908263203 Simplifying x = 119.908263203Subproblem 2
x + -60 = -59.908263203 Simplifying x + -60 = -59.908263203 Reorder the terms: -60 + x = -59.908263203 Solving -60 + x = -59.908263203 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 = -59.908263203 + 60 Combine like terms: -60 + 60 = 0 0 + x = -59.908263203 + 60 x = -59.908263203 + 60 Combine like terms: -59.908263203 + 60 = 0.091736797 x = 0.091736797 Simplifying x = 0.091736797Solution
The solution to the problem is based on the solutions from the subproblems. x = {119.908263203, 0.091736797}
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