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Simplifying 600x + -3x2 + -12000 = 0 Reorder the terms: -12000 + 600x + -3x2 = 0 Solving -12000 + 600x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4000 + 200x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4000 + 200x + -1x2)' equal to zero and attempt to solve: Simplifying -4000 + 200x + -1x2 = 0 Solving -4000 + 200x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4000 + -200x + x2 = 0 Move the constant term to the right: Add '-4000' to each side of the equation. 4000 + -200x + -4000 + x2 = 0 + -4000 Reorder the terms: 4000 + -4000 + -200x + x2 = 0 + -4000 Combine like terms: 4000 + -4000 = 0 0 + -200x + x2 = 0 + -4000 -200x + x2 = 0 + -4000 Combine like terms: 0 + -4000 = -4000 -200x + x2 = -4000 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -4000 + 10000 Reorder the terms: 10000 + -200x + x2 = -4000 + 10000 Combine like terms: -4000 + 10000 = 6000 10000 + -200x + x2 = 6000 Factor a perfect square on the left side: (x + -100)(x + -100) = 6000 Calculate the square root of the right side: 77.459666924 Break this problem into two subproblems by setting (x + -100) equal to 77.459666924 and -77.459666924.Subproblem 1
x + -100 = 77.459666924 Simplifying x + -100 = 77.459666924 Reorder the terms: -100 + x = 77.459666924 Solving -100 + x = 77.459666924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 77.459666924 + 100 Combine like terms: -100 + 100 = 0 0 + x = 77.459666924 + 100 x = 77.459666924 + 100 Combine like terms: 77.459666924 + 100 = 177.459666924 x = 177.459666924 Simplifying x = 177.459666924Subproblem 2
x + -100 = -77.459666924 Simplifying x + -100 = -77.459666924 Reorder the terms: -100 + x = -77.459666924 Solving -100 + x = -77.459666924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -77.459666924 + 100 Combine like terms: -100 + 100 = 0 0 + x = -77.459666924 + 100 x = -77.459666924 + 100 Combine like terms: -77.459666924 + 100 = 22.540333076 x = 22.540333076 Simplifying x = 22.540333076Solution
The solution to the problem is based on the solutions from the subproblems. x = {177.459666924, 22.540333076}Solution
x = {177.459666924, 22.540333076}
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