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Simplifying -1x2 + 120x + 600 = 0 Reorder the terms: 600 + 120x + -1x2 = 0 Solving 600 + 120x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -600 + -120x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + -120x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -120x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -120x + x2 = 0 + 600 -120x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -120x + x2 = 600 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 = 600 + 3600 Reorder the terms: 3600 + -120x + x2 = 600 + 3600 Combine like terms: 600 + 3600 = 4200 3600 + -120x + x2 = 4200 Factor a perfect square on the left side: (x + -60)(x + -60) = 4200 Calculate the square root of the right side: 64.807406984 Break this problem into two subproblems by setting (x + -60) equal to 64.807406984 and -64.807406984.Subproblem 1
x + -60 = 64.807406984 Simplifying x + -60 = 64.807406984 Reorder the terms: -60 + x = 64.807406984 Solving -60 + x = 64.807406984 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 = 64.807406984 + 60 Combine like terms: -60 + 60 = 0 0 + x = 64.807406984 + 60 x = 64.807406984 + 60 Combine like terms: 64.807406984 + 60 = 124.807406984 x = 124.807406984 Simplifying x = 124.807406984Subproblem 2
x + -60 = -64.807406984 Simplifying x + -60 = -64.807406984 Reorder the terms: -60 + x = -64.807406984 Solving -60 + x = -64.807406984 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 = -64.807406984 + 60 Combine like terms: -60 + 60 = 0 0 + x = -64.807406984 + 60 x = -64.807406984 + 60 Combine like terms: -64.807406984 + 60 = -4.807406984 x = -4.807406984 Simplifying x = -4.807406984Solution
The solution to the problem is based on the solutions from the subproblems. x = {124.807406984, -4.807406984}
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