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Simplifying 6x3 + 54x2 + -6x = 0 Reorder the terms: -6x + 54x2 + 6x3 = 0 Solving -6x + 54x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-1 + 9x + x2) = 0 Ignore the factor 6.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 '(-1 + 9x + x2)' equal to zero and attempt to solve: Simplifying -1 + 9x + x2 = 0 Solving -1 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 9x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 9x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9x + x2 = 0 + 1 9x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 9x + x2 = 1 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 1 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + 9x + x2 = 21.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 4.5 = 4.609772229 Simplifying x + 4.5 = 4.609772229 Reorder the terms: 4.5 + x = 4.609772229 Solving 4.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.609772229 + -4.5 x = 4.609772229 + -4.5 Combine like terms: 4.609772229 + -4.5 = 0.109772229 x = 0.109772229 Simplifying x = 0.109772229Subproblem 2
x + 4.5 = -4.609772229 Simplifying x + 4.5 = -4.609772229 Reorder the terms: 4.5 + x = -4.609772229 Solving 4.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.609772229 + -4.5 x = -4.609772229 + -4.5 Combine like terms: -4.609772229 + -4.5 = -9.109772229 x = -9.109772229 Simplifying x = -9.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.109772229, -9.109772229}Solution
x = {0, 0.109772229, -9.109772229}
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