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Simplifying 18x2 + 6400x + -120800 = 0 Reorder the terms: -120800 + 6400x + 18x2 = 0 Solving -120800 + 6400x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60400 + 3200x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60400 + 3200x + 9x2)' equal to zero and attempt to solve: Simplifying -60400 + 3200x + 9x2 = 0 Solving -60400 + 3200x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6711.111111 + 355.5555556x + x2 = 0 Move the constant term to the right: Add '6711.111111' to each side of the equation. -6711.111111 + 355.5555556x + 6711.111111 + x2 = 0 + 6711.111111 Reorder the terms: -6711.111111 + 6711.111111 + 355.5555556x + x2 = 0 + 6711.111111 Combine like terms: -6711.111111 + 6711.111111 = 0.000000 0.000000 + 355.5555556x + x2 = 0 + 6711.111111 355.5555556x + x2 = 0 + 6711.111111 Combine like terms: 0 + 6711.111111 = 6711.111111 355.5555556x + x2 = 6711.111111 The x term is 355.5555556x. Take half its coefficient (177.7777778). Square it (31604.93828) and add it to both sides. Add '31604.93828' to each side of the equation. 355.5555556x + 31604.93828 + x2 = 6711.111111 + 31604.93828 Reorder the terms: 31604.93828 + 355.5555556x + x2 = 6711.111111 + 31604.93828 Combine like terms: 6711.111111 + 31604.93828 = 38316.049391 31604.93828 + 355.5555556x + x2 = 38316.049391 Factor a perfect square on the left side: (x + 177.7777778)(x + 177.7777778) = 38316.049391 Calculate the square root of the right side: 195.744857892 Break this problem into two subproblems by setting (x + 177.7777778) equal to 195.744857892 and -195.744857892.Subproblem 1
x + 177.7777778 = 195.744857892 Simplifying x + 177.7777778 = 195.744857892 Reorder the terms: 177.7777778 + x = 195.744857892 Solving 177.7777778 + x = 195.744857892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-177.7777778' to each side of the equation. 177.7777778 + -177.7777778 + x = 195.744857892 + -177.7777778 Combine like terms: 177.7777778 + -177.7777778 = 0.0000000 0.0000000 + x = 195.744857892 + -177.7777778 x = 195.744857892 + -177.7777778 Combine like terms: 195.744857892 + -177.7777778 = 17.967080092 x = 17.967080092 Simplifying x = 17.967080092Subproblem 2
x + 177.7777778 = -195.744857892 Simplifying x + 177.7777778 = -195.744857892 Reorder the terms: 177.7777778 + x = -195.744857892 Solving 177.7777778 + x = -195.744857892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-177.7777778' to each side of the equation. 177.7777778 + -177.7777778 + x = -195.744857892 + -177.7777778 Combine like terms: 177.7777778 + -177.7777778 = 0.0000000 0.0000000 + x = -195.744857892 + -177.7777778 x = -195.744857892 + -177.7777778 Combine like terms: -195.744857892 + -177.7777778 = -373.522635692 x = -373.522635692 Simplifying x = -373.522635692Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.967080092, -373.522635692}Solution
x = {17.967080092, -373.522635692}
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