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Simplifying 240x3 + 540x2 + -2160x = 0 Reorder the terms: -2160x + 540x2 + 240x3 = 0 Solving -2160x + 540x2 + 240x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '60x'. 60x(-36 + 9x + 4x2) = 0 Ignore the factor 60.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-36 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying -36 + 9x + 4x2 = 0 Solving -36 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9 + 2.25x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 2.25x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 2.25x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2.25x + x2 = 0 + 9 2.25x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 2.25x + x2 = 9 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 9 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 9 + 1.265625 Combine like terms: 9 + 1.265625 = 10.265625 1.265625 + 2.25x + x2 = 10.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + 1.125) equal to 3.204001404 and -3.204001404.Subproblem 1
x + 1.125 = 3.204001404 Simplifying x + 1.125 = 3.204001404 Reorder the terms: 1.125 + x = 3.204001404 Solving 1.125 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 3.204001404 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 3.204001404 + -1.125 x = 3.204001404 + -1.125 Combine like terms: 3.204001404 + -1.125 = 2.079001404 x = 2.079001404 Simplifying x = 2.079001404Subproblem 2
x + 1.125 = -3.204001404 Simplifying x + 1.125 = -3.204001404 Reorder the terms: 1.125 + x = -3.204001404 Solving 1.125 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -3.204001404 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -3.204001404 + -1.125 x = -3.204001404 + -1.125 Combine like terms: -3.204001404 + -1.125 = -4.329001404 x = -4.329001404 Simplifying x = -4.329001404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.079001404, -4.329001404}Solution
x = {0, 2.079001404, -4.329001404}
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