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Simplifying 24000 = 6x2 + -3x + 6 Reorder the terms: 24000 = 6 + -3x + 6x2 Solving 24000 = 6 + -3x + 6x2 Solving for variable 'x'. Combine like terms: 24000 + -6 = 23994 23994 + 3x + -6x2 = 6 + -3x + 6x2 + -6 + 3x + -6x2 Reorder the terms: 23994 + 3x + -6x2 = 6 + -6 + -3x + 3x + 6x2 + -6x2 Combine like terms: 6 + -6 = 0 23994 + 3x + -6x2 = 0 + -3x + 3x + 6x2 + -6x2 23994 + 3x + -6x2 = -3x + 3x + 6x2 + -6x2 Combine like terms: -3x + 3x = 0 23994 + 3x + -6x2 = 0 + 6x2 + -6x2 23994 + 3x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 23994 + 3x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7998 + x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7998 + x + -2x2)' equal to zero and attempt to solve: Simplifying 7998 + x + -2x2 = 0 Solving 7998 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3999 + -0.5x + x2 = 0 Move the constant term to the right: Add '3999' to each side of the equation. -3999 + -0.5x + 3999 + x2 = 0 + 3999 Reorder the terms: -3999 + 3999 + -0.5x + x2 = 0 + 3999 Combine like terms: -3999 + 3999 = 0 0 + -0.5x + x2 = 0 + 3999 -0.5x + x2 = 0 + 3999 Combine like terms: 0 + 3999 = 3999 -0.5x + x2 = 3999 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = 3999 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 3999 + 0.25 Combine like terms: 3999 + 0.25 = 3999.25 0.25 + -0.5x + x2 = 3999.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3999.25 Calculate the square root of the right side: 63.239623655 Break this problem into two subproblems by setting (x + 0.5) equal to 63.239623655 and -63.239623655.Subproblem 1
x + 0.5 = 63.239623655 Simplifying x + 0.5 = 63.239623655 Reorder the terms: 0.5 + x = 63.239623655 Solving 0.5 + x = 63.239623655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 63.239623655 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 63.239623655 + -0.5 x = 63.239623655 + -0.5 Combine like terms: 63.239623655 + -0.5 = 62.739623655 x = 62.739623655 Simplifying x = 62.739623655Subproblem 2
x + 0.5 = -63.239623655 Simplifying x + 0.5 = -63.239623655 Reorder the terms: 0.5 + x = -63.239623655 Solving 0.5 + x = -63.239623655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -63.239623655 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -63.239623655 + -0.5 x = -63.239623655 + -0.5 Combine like terms: -63.239623655 + -0.5 = -63.739623655 x = -63.739623655 Simplifying x = -63.739623655Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.739623655, -63.739623655}Solution
x = {62.739623655, -63.739623655}
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