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Simplifying 2x2 + -240x + 325 = 0 Reorder the terms: 325 + -240x + 2x2 = 0 Solving 325 + -240x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 162.5 + -120x + x2 = 0 Move the constant term to the right: Add '-162.5' to each side of the equation. 162.5 + -120x + -162.5 + x2 = 0 + -162.5 Reorder the terms: 162.5 + -162.5 + -120x + x2 = 0 + -162.5 Combine like terms: 162.5 + -162.5 = 0.0 0.0 + -120x + x2 = 0 + -162.5 -120x + x2 = 0 + -162.5 Combine like terms: 0 + -162.5 = -162.5 -120x + x2 = -162.5 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 = -162.5 + 3600 Reorder the terms: 3600 + -120x + x2 = -162.5 + 3600 Combine like terms: -162.5 + 3600 = 3437.5 3600 + -120x + x2 = 3437.5 Factor a perfect square on the left side: (x + -60)(x + -60) = 3437.5 Calculate the square root of the right side: 58.630196998 Break this problem into two subproblems by setting (x + -60) equal to 58.630196998 and -58.630196998.Subproblem 1
x + -60 = 58.630196998 Simplifying x + -60 = 58.630196998 Reorder the terms: -60 + x = 58.630196998 Solving -60 + x = 58.630196998 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 = 58.630196998 + 60 Combine like terms: -60 + 60 = 0 0 + x = 58.630196998 + 60 x = 58.630196998 + 60 Combine like terms: 58.630196998 + 60 = 118.630196998 x = 118.630196998 Simplifying x = 118.630196998Subproblem 2
x + -60 = -58.630196998 Simplifying x + -60 = -58.630196998 Reorder the terms: -60 + x = -58.630196998 Solving -60 + x = -58.630196998 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 = -58.630196998 + 60 Combine like terms: -60 + 60 = 0 0 + x = -58.630196998 + 60 x = -58.630196998 + 60 Combine like terms: -58.630196998 + 60 = 1.369803002 x = 1.369803002 Simplifying x = 1.369803002Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.630196998, 1.369803002}
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