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Simplifying 1.5(x2) + -180x + 1000 = 0 Reorder the terms: 1000 + -180x + 1.5x2 = 0 Solving 1000 + -180x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 666.6666667 + -120x + x2 = 0 Move the constant term to the right: Add '-666.6666667' to each side of the equation. 666.6666667 + -120x + -666.6666667 + x2 = 0 + -666.6666667 Reorder the terms: 666.6666667 + -666.6666667 + -120x + x2 = 0 + -666.6666667 Combine like terms: 666.6666667 + -666.6666667 = 0.0000000 0.0000000 + -120x + x2 = 0 + -666.6666667 -120x + x2 = 0 + -666.6666667 Combine like terms: 0 + -666.6666667 = -666.6666667 -120x + x2 = -666.6666667 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 = -666.6666667 + 3600 Reorder the terms: 3600 + -120x + x2 = -666.6666667 + 3600 Combine like terms: -666.6666667 + 3600 = 2933.3333333 3600 + -120x + x2 = 2933.3333333 Factor a perfect square on the left side: (x + -60)(x + -60) = 2933.3333333 Calculate the square root of the right side: 54.160256031 Break this problem into two subproblems by setting (x + -60) equal to 54.160256031 and -54.160256031.Subproblem 1
x + -60 = 54.160256031 Simplifying x + -60 = 54.160256031 Reorder the terms: -60 + x = 54.160256031 Solving -60 + x = 54.160256031 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 = 54.160256031 + 60 Combine like terms: -60 + 60 = 0 0 + x = 54.160256031 + 60 x = 54.160256031 + 60 Combine like terms: 54.160256031 + 60 = 114.160256031 x = 114.160256031 Simplifying x = 114.160256031Subproblem 2
x + -60 = -54.160256031 Simplifying x + -60 = -54.160256031 Reorder the terms: -60 + x = -54.160256031 Solving -60 + x = -54.160256031 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 = -54.160256031 + 60 Combine like terms: -60 + 60 = 0 0 + x = -54.160256031 + 60 x = -54.160256031 + 60 Combine like terms: -54.160256031 + 60 = 5.839743969 x = 5.839743969 Simplifying x = 5.839743969Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.160256031, 5.839743969}
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