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Simplifying x3 + -12x2 + x = 0 Reorder the terms: x + -12x2 + x3 = 0 Solving x + -12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -12x + 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 '(1 + -12x + x2)' equal to zero and attempt to solve: Simplifying 1 + -12x + x2 = 0 Solving 1 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -12x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -12x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12x + x2 = 0 + -1 -12x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -12x + x2 = -1 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -1 + 36 Reorder the terms: 36 + -12x + x2 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + -12x + x2 = 35 Factor a perfect square on the left side: (x + -6)(x + -6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -6) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -6 = 5.916079783 Simplifying x + -6 = 5.916079783 Reorder the terms: -6 + x = 5.916079783 Solving -6 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.916079783 + 6 x = 5.916079783 + 6 Combine like terms: 5.916079783 + 6 = 11.916079783 x = 11.916079783 Simplifying x = 11.916079783Subproblem 2
x + -6 = -5.916079783 Simplifying x + -6 = -5.916079783 Reorder the terms: -6 + x = -5.916079783 Solving -6 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.916079783 + 6 x = -5.916079783 + 6 Combine like terms: -5.916079783 + 6 = 0.083920217 x = 0.083920217 Simplifying x = 0.083920217Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.916079783, 0.083920217}Solution
x = {0, 11.916079783, 0.083920217}
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