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Simplifying x3 + 12x2 + -72x = 0 Reorder the terms: -72x + 12x2 + x3 = 0 Solving -72x + 12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-72 + 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 '(-72 + 12x + x2)' equal to zero and attempt to solve: Simplifying -72 + 12x + x2 = 0 Solving -72 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 12x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 12x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 12x + x2 = 0 + 72 12x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 12x + x2 = 72 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 = 72 + 36 Reorder the terms: 36 + 12x + x2 = 72 + 36 Combine like terms: 72 + 36 = 108 36 + 12x + x2 = 108 Factor a perfect square on the left side: (x + 6)(x + 6) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + 6) equal to 10.392304845 and -10.392304845.Subproblem 1
x + 6 = 10.392304845 Simplifying x + 6 = 10.392304845 Reorder the terms: 6 + x = 10.392304845 Solving 6 + x = 10.392304845 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 = 10.392304845 + -6 Combine like terms: 6 + -6 = 0 0 + x = 10.392304845 + -6 x = 10.392304845 + -6 Combine like terms: 10.392304845 + -6 = 4.392304845 x = 4.392304845 Simplifying x = 4.392304845Subproblem 2
x + 6 = -10.392304845 Simplifying x + 6 = -10.392304845 Reorder the terms: 6 + x = -10.392304845 Solving 6 + x = -10.392304845 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 = -10.392304845 + -6 Combine like terms: 6 + -6 = 0 0 + x = -10.392304845 + -6 x = -10.392304845 + -6 Combine like terms: -10.392304845 + -6 = -16.392304845 x = -16.392304845 Simplifying x = -16.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.392304845, -16.392304845}Solution
x = {0, 4.392304845, -16.392304845}
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