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Simplifying x3(x2 + -7) + -36x = 0 Reorder the terms: x3(-7 + x2) + -36x = 0 (-7 * x3 + x2 * x3) + -36x = 0 (-7x3 + x5) + -36x = 0 Reorder the terms: -36x + -7x3 + x5 = 0 Solving -36x + -7x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + -7x2 + x4) = 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 + -7x2 + x4)' equal to zero and attempt to solve: Simplifying -36 + -7x2 + x4 = 0 Solving -36 + -7x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -7x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -7x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -7x2 + x4 = 0 + 36 -7x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -7x2 + x4 = 36 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = 36 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = 36 + 12.25 Combine like terms: 36 + 12.25 = 48.25 12.25 + -7x2 + x4 = 48.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x2 + -3.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x2 + -3.5 = 6.946221995 Simplifying x2 + -3.5 = 6.946221995 Reorder the terms: -3.5 + x2 = 6.946221995 Solving -3.5 + x2 = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 6.946221995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 6.946221995 + 3.5 x2 = 6.946221995 + 3.5 Combine like terms: 6.946221995 + 3.5 = 10.446221995 x2 = 10.446221995 Simplifying x2 = 10.446221995 Take the square root of each side: x = {-3.23206157, 3.23206157}Subproblem 2
x2 + -3.5 = -6.946221995 Simplifying x2 + -3.5 = -6.946221995 Reorder the terms: -3.5 + x2 = -6.946221995 Solving -3.5 + x2 = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -6.946221995 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -6.946221995 + 3.5 x2 = -6.946221995 + 3.5 Combine like terms: -6.946221995 + 3.5 = -3.446221995 x2 = -3.446221995 Simplifying x2 = -3.446221995 Reorder the terms: 3.446221995 + x2 = -3.446221995 + 3.446221995 Combine like terms: -3.446221995 + 3.446221995 = 0.000000000 3.446221995 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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