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Simplifying 355.5 = -2x * x + 240x Multiply x * x 355.5 = -2x2 + 240x Reorder the terms: 355.5 = 240x + -2x2 Solving 355.5 = 240x + -2x2 Solving for variable 'x'. Reorder the terms: 355.5 + -240x + 2x2 = 240x + -240x + -2x2 + 2x2 Combine like terms: 240x + -240x = 0 355.5 + -240x + 2x2 = 0 + -2x2 + 2x2 355.5 + -240x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 355.5 + -240x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 177.75 + -120x + x2 = 0 Move the constant term to the right: Add '-177.75' to each side of the equation. 177.75 + -120x + -177.75 + x2 = 0 + -177.75 Reorder the terms: 177.75 + -177.75 + -120x + x2 = 0 + -177.75 Combine like terms: 177.75 + -177.75 = 0.00 0.00 + -120x + x2 = 0 + -177.75 -120x + x2 = 0 + -177.75 Combine like terms: 0 + -177.75 = -177.75 -120x + x2 = -177.75 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 = -177.75 + 3600 Reorder the terms: 3600 + -120x + x2 = -177.75 + 3600 Combine like terms: -177.75 + 3600 = 3422.25 3600 + -120x + x2 = 3422.25 Factor a perfect square on the left side: (x + -60)(x + -60) = 3422.25 Calculate the square root of the right side: 58.5 Break this problem into two subproblems by setting (x + -60) equal to 58.5 and -58.5.Subproblem 1
x + -60 = 58.5 Simplifying x + -60 = 58.5 Reorder the terms: -60 + x = 58.5 Solving -60 + x = 58.5 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 = 58.5 + 60 Combine like terms: -60 + 60 = 0 0 + x = 58.5 + 60 x = 58.5 + 60 Combine like terms: 58.5 + 60 = 118.5 x = 118.5 Simplifying x = 118.5Subproblem 2
x + -60 = -58.5 Simplifying x + -60 = -58.5 Reorder the terms: -60 + x = -58.5 Solving -60 + x = -58.5 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 = -58.5 + 60 Combine like terms: -60 + 60 = 0 0 + x = -58.5 + 60 x = -58.5 + 60 Combine like terms: -58.5 + 60 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.5, 1.5}
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