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Simplifying x3 + 12x2 + 30x = 0 Reorder the terms: 30x + 12x2 + x3 = 0 Solving 30x + 12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(30 + 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 '(30 + 12x + x2)' equal to zero and attempt to solve: Simplifying 30 + 12x + x2 = 0 Solving 30 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 12x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 12x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 12x + x2 = 0 + -30 12x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 12x + x2 = -30 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 = -30 + 36 Reorder the terms: 36 + 12x + x2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + 12x + x2 = 6 Factor a perfect square on the left side: (x + 6)(x + 6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 6) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 6 = 2.449489743 Simplifying x + 6 = 2.449489743 Reorder the terms: 6 + x = 2.449489743 Solving 6 + x = 2.449489743 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 = 2.449489743 + -6 Combine like terms: 6 + -6 = 0 0 + x = 2.449489743 + -6 x = 2.449489743 + -6 Combine like terms: 2.449489743 + -6 = -3.550510257 x = -3.550510257 Simplifying x = -3.550510257Subproblem 2
x + 6 = -2.449489743 Simplifying x + 6 = -2.449489743 Reorder the terms: 6 + x = -2.449489743 Solving 6 + x = -2.449489743 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 = -2.449489743 + -6 Combine like terms: 6 + -6 = 0 0 + x = -2.449489743 + -6 x = -2.449489743 + -6 Combine like terms: -2.449489743 + -6 = -8.449489743 x = -8.449489743 Simplifying x = -8.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.550510257, -8.449489743}Solution
x = {0, -3.550510257, -8.449489743}
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