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Simplifying x3 + 12x2 + -27x = 0 Reorder the terms: -27x + 12x2 + x3 = 0 Solving -27x + 12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-27 + 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 '(-27 + 12x + x2)' equal to zero and attempt to solve: Simplifying -27 + 12x + x2 = 0 Solving -27 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 12x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 12x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 12x + x2 = 0 + 27 12x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 12x + x2 = 27 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 = 27 + 36 Reorder the terms: 36 + 12x + x2 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + 12x + x2 = 63 Factor a perfect square on the left side: (x + 6)(x + 6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 6) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 6 = 7.937253933 Simplifying x + 6 = 7.937253933 Reorder the terms: 6 + x = 7.937253933 Solving 6 + x = 7.937253933 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 = 7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.937253933 + -6 x = 7.937253933 + -6 Combine like terms: 7.937253933 + -6 = 1.937253933 x = 1.937253933 Simplifying x = 1.937253933Subproblem 2
x + 6 = -7.937253933 Simplifying x + 6 = -7.937253933 Reorder the terms: 6 + x = -7.937253933 Solving 6 + x = -7.937253933 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 = -7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.937253933 + -6 x = -7.937253933 + -6 Combine like terms: -7.937253933 + -6 = -13.937253933 x = -13.937253933 Simplifying x = -13.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.937253933, -13.937253933}Solution
x = {0, 1.937253933, -13.937253933}
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