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Simplifying -1.5x2 + 2000x + -600 = 0 Reorder the terms: -600 + 2000x + -1.5x2 = 0 Solving -600 + 2000x + -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'. 400 + -1333.333333x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -1333.333333x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -1333.333333x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -1333.333333x + x2 = 0 + -400 -1333.333333x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -1333.333333x + x2 = -400 The x term is -1333.333333x. Take half its coefficient (-666.6666665). Square it (444444.4442) and add it to both sides. Add '444444.4442' to each side of the equation. -1333.333333x + 444444.4442 + x2 = -400 + 444444.4442 Reorder the terms: 444444.4442 + -1333.333333x + x2 = -400 + 444444.4442 Combine like terms: -400 + 444444.4442 = 444044.4442 444444.4442 + -1333.333333x + x2 = 444044.4442 Factor a perfect square on the left side: (x + -666.6666665)(x + -666.6666665) = 444044.4442 Calculate the square root of the right side: 666.366598953 Break this problem into two subproblems by setting (x + -666.6666665) equal to 666.366598953 and -666.366598953.Subproblem 1
x + -666.6666665 = 666.366598953 Simplifying x + -666.6666665 = 666.366598953 Reorder the terms: -666.6666665 + x = 666.366598953 Solving -666.6666665 + x = 666.366598953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '666.6666665' to each side of the equation. -666.6666665 + 666.6666665 + x = 666.366598953 + 666.6666665 Combine like terms: -666.6666665 + 666.6666665 = 0.0000000 0.0000000 + x = 666.366598953 + 666.6666665 x = 666.366598953 + 666.6666665 Combine like terms: 666.366598953 + 666.6666665 = 1333.033265453 x = 1333.033265453 Simplifying x = 1333.033265453Subproblem 2
x + -666.6666665 = -666.366598953 Simplifying x + -666.6666665 = -666.366598953 Reorder the terms: -666.6666665 + x = -666.366598953 Solving -666.6666665 + x = -666.366598953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '666.6666665' to each side of the equation. -666.6666665 + 666.6666665 + x = -666.366598953 + 666.6666665 Combine like terms: -666.6666665 + 666.6666665 = 0.0000000 0.0000000 + x = -666.366598953 + 666.6666665 x = -666.366598953 + 666.6666665 Combine like terms: -666.366598953 + 666.6666665 = 0.300067547 x = 0.300067547 Simplifying x = 0.300067547Solution
The solution to the problem is based on the solutions from the subproblems. x = {1333.033265453, 0.300067547}
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