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Simplifying x3 + 12x2 + 16x = 0 Reorder the terms: 16x + 12x2 + x3 = 0 Solving 16x + 12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(16 + 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 '(16 + 12x + x2)' equal to zero and attempt to solve: Simplifying 16 + 12x + x2 = 0 Solving 16 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 12x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 12x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 12x + x2 = 0 + -16 12x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 12x + x2 = -16 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 = -16 + 36 Reorder the terms: 36 + 12x + x2 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + 12x + x2 = 20 Factor a perfect square on the left side: (x + 6)(x + 6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 6) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 6 = 4.472135955 Simplifying x + 6 = 4.472135955 Reorder the terms: 6 + x = 4.472135955 Solving 6 + x = 4.472135955 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 = 4.472135955 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.472135955 + -6 x = 4.472135955 + -6 Combine like terms: 4.472135955 + -6 = -1.527864045 x = -1.527864045 Simplifying x = -1.527864045Subproblem 2
x + 6 = -4.472135955 Simplifying x + 6 = -4.472135955 Reorder the terms: 6 + x = -4.472135955 Solving 6 + x = -4.472135955 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 = -4.472135955 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.472135955 + -6 x = -4.472135955 + -6 Combine like terms: -4.472135955 + -6 = -10.472135955 x = -10.472135955 Simplifying x = -10.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.527864045, -10.472135955}Solution
x = {0, -1.527864045, -10.472135955}
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