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Simplifying 5400 = x(180 + -1.5x) 5400 = (180 * x + -1.5x * x) 5400 = (180x + -1.5x2) Solving 5400 = 180x + -1.5x2 Solving for variable 'x'. Reorder the terms: 5400 + -180x + 1.5x2 = 180x + -180x + -1.5x2 + 1.5x2 Combine like terms: 180x + -180x = 0 5400 + -180x + 1.5x2 = 0 + -1.5x2 + 1.5x2 5400 + -180x + 1.5x2 = -1.5x2 + 1.5x2 Combine like terms: -1.5x2 + 1.5x2 = 0.0 5400 + -180x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 3600 + -120x + x2 = 0 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 = 0 3600 + -120x + x2 = 0 Factor a perfect square on the left side: (x + -60)(x + -60) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -60) equal to 0 and 0.Subproblem 1
x + -60 = 0 Simplifying x + -60 = 0 Reorder the terms: -60 + x = 0 Solving -60 + x = 0 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 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + x = 0 + 60 x = 0 + 60 Combine like terms: 0 + 60 = 60 x = 60 Simplifying x = 60Subproblem 2
x + -60 = 0 Simplifying x + -60 = 0 Reorder the terms: -60 + x = 0 Solving -60 + x = 0 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 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + x = 0 + 60 x = 0 + 60 Combine like terms: 0 + 60 = 60 x = 60 Simplifying x = 60Solution
The solution to the problem is based on the solutions from the subproblems. x = {60, 60}
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