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Simplifying -32x2 + 3600x + 396000 = 0 Reorder the terms: 396000 + 3600x + -32x2 = 0 Solving 396000 + 3600x + -32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(24750 + 225x + -2x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(24750 + 225x + -2x2)' equal to zero and attempt to solve: Simplifying 24750 + 225x + -2x2 = 0 Solving 24750 + 225x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12375 + -112.5x + x2 = 0 Move the constant term to the right: Add '12375' to each side of the equation. -12375 + -112.5x + 12375 + x2 = 0 + 12375 Reorder the terms: -12375 + 12375 + -112.5x + x2 = 0 + 12375 Combine like terms: -12375 + 12375 = 0 0 + -112.5x + x2 = 0 + 12375 -112.5x + x2 = 0 + 12375 Combine like terms: 0 + 12375 = 12375 -112.5x + x2 = 12375 The x term is -112.5x. Take half its coefficient (-56.25). Square it (3164.0625) and add it to both sides. Add '3164.0625' to each side of the equation. -112.5x + 3164.0625 + x2 = 12375 + 3164.0625 Reorder the terms: 3164.0625 + -112.5x + x2 = 12375 + 3164.0625 Combine like terms: 12375 + 3164.0625 = 15539.0625 3164.0625 + -112.5x + x2 = 15539.0625 Factor a perfect square on the left side: (x + -56.25)(x + -56.25) = 15539.0625 Calculate the square root of the right side: 124.655776039 Break this problem into two subproblems by setting (x + -56.25) equal to 124.655776039 and -124.655776039.Subproblem 1
x + -56.25 = 124.655776039 Simplifying x + -56.25 = 124.655776039 Reorder the terms: -56.25 + x = 124.655776039 Solving -56.25 + x = 124.655776039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.25' to each side of the equation. -56.25 + 56.25 + x = 124.655776039 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + x = 124.655776039 + 56.25 x = 124.655776039 + 56.25 Combine like terms: 124.655776039 + 56.25 = 180.905776039 x = 180.905776039 Simplifying x = 180.905776039Subproblem 2
x + -56.25 = -124.655776039 Simplifying x + -56.25 = -124.655776039 Reorder the terms: -56.25 + x = -124.655776039 Solving -56.25 + x = -124.655776039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56.25' to each side of the equation. -56.25 + 56.25 + x = -124.655776039 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + x = -124.655776039 + 56.25 x = -124.655776039 + 56.25 Combine like terms: -124.655776039 + 56.25 = -68.405776039 x = -68.405776039 Simplifying x = -68.405776039Solution
The solution to the problem is based on the solutions from the subproblems. x = {180.905776039, -68.405776039}Solution
x = {180.905776039, -68.405776039}
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