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Simplifying x3 + 12x2 + -2x = 0 Reorder the terms: -2x + 12x2 + x3 = 0 Solving -2x + 12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 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 '(-2 + 12x + x2)' equal to zero and attempt to solve: Simplifying -2 + 12x + x2 = 0 Solving -2 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 12x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 12x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 12x + x2 = 0 + 2 12x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 12x + x2 = 2 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 = 2 + 36 Reorder the terms: 36 + 12x + x2 = 2 + 36 Combine like terms: 2 + 36 = 38 36 + 12x + x2 = 38 Factor a perfect square on the left side: (x + 6)(x + 6) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 6) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 6 = 6.164414003 Simplifying x + 6 = 6.164414003 Reorder the terms: 6 + x = 6.164414003 Solving 6 + x = 6.164414003 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 = 6.164414003 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.164414003 + -6 x = 6.164414003 + -6 Combine like terms: 6.164414003 + -6 = 0.164414003 x = 0.164414003 Simplifying x = 0.164414003Subproblem 2
x + 6 = -6.164414003 Simplifying x + 6 = -6.164414003 Reorder the terms: 6 + x = -6.164414003 Solving 6 + x = -6.164414003 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 = -6.164414003 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.164414003 + -6 x = -6.164414003 + -6 Combine like terms: -6.164414003 + -6 = -12.164414003 x = -12.164414003 Simplifying x = -12.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.164414003, -12.164414003}Solution
x = {0, 0.164414003, -12.164414003}
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