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Simplifying x3 + -3x2 + -36x = 0 Reorder the terms: -36x + -3x2 + x3 = 0 Solving -36x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + -3x + x2) = 0Subproblem 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 + -3x + x2)' equal to zero and attempt to solve: Simplifying -36 + -3x + x2 = 0 Solving -36 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -3x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -3x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -3x + x2 = 0 + 36 -3x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -3x + x2 = 36 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 36 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 36 + 2.25 Combine like terms: 36 + 2.25 = 38.25 2.25 + -3x + x2 = 38.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -1.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -1.5 = 6.184658438 Simplifying x + -1.5 = 6.184658438 Reorder the terms: -1.5 + x = 6.184658438 Solving -1.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.184658438 + 1.5 x = 6.184658438 + 1.5 Combine like terms: 6.184658438 + 1.5 = 7.684658438 x = 7.684658438 Simplifying x = 7.684658438Subproblem 2
x + -1.5 = -6.184658438 Simplifying x + -1.5 = -6.184658438 Reorder the terms: -1.5 + x = -6.184658438 Solving -1.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.184658438 + 1.5 x = -6.184658438 + 1.5 Combine like terms: -6.184658438 + 1.5 = -4.684658438 x = -4.684658438 Simplifying x = -4.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.684658438, -4.684658438}Solution
x = {0, 7.684658438, -4.684658438}
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