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Simplifying -3x2 + -32x + 2000 = 0 Reorder the terms: 2000 + -32x + -3x2 = 0 Solving 2000 + -32x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -666.6666667 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + 10.66666667x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + 10.66666667x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + 10.66666667x + x2 = 0 + 666.6666667 10.66666667x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 10.66666667x + x2 = 666.6666667 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = 666.6666667 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = 666.6666667 + 28.44444446 Combine like terms: 666.6666667 + 28.44444446 = 695.11111116 28.44444446 + 10.66666667x + x2 = 695.11111116 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 695.11111116 Calculate the square root of the right side: 26.364959912 Break this problem into two subproblems by setting (x + 5.333333335) equal to 26.364959912 and -26.364959912.Subproblem 1
x + 5.333333335 = 26.364959912 Simplifying x + 5.333333335 = 26.364959912 Reorder the terms: 5.333333335 + x = 26.364959912 Solving 5.333333335 + x = 26.364959912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 26.364959912 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 26.364959912 + -5.333333335 x = 26.364959912 + -5.333333335 Combine like terms: 26.364959912 + -5.333333335 = 21.031626577 x = 21.031626577 Simplifying x = 21.031626577Subproblem 2
x + 5.333333335 = -26.364959912 Simplifying x + 5.333333335 = -26.364959912 Reorder the terms: 5.333333335 + x = -26.364959912 Solving 5.333333335 + x = -26.364959912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -26.364959912 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -26.364959912 + -5.333333335 x = -26.364959912 + -5.333333335 Combine like terms: -26.364959912 + -5.333333335 = -31.698293247 x = -31.698293247 Simplifying x = -31.698293247Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.031626577, -31.698293247}
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