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Simplifying x3 + 16x2 + 36x = 0 Reorder the terms: 36x + 16x2 + x3 = 0 Solving 36x + 16x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(36 + 16x + 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 '(36 + 16x + x2)' equal to zero and attempt to solve: Simplifying 36 + 16x + x2 = 0 Solving 36 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 16x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 16x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 16x + x2 = 0 + -36 16x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 16x + x2 = -36 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -36 + 64 Reorder the terms: 64 + 16x + x2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + 16x + x2 = 28 Factor a perfect square on the left side: (x + 8)(x + 8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 8) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 8 = 5.291502622 Simplifying x + 8 = 5.291502622 Reorder the terms: 8 + x = 5.291502622 Solving 8 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.291502622 + -8 x = 5.291502622 + -8 Combine like terms: 5.291502622 + -8 = -2.708497378 x = -2.708497378 Simplifying x = -2.708497378Subproblem 2
x + 8 = -5.291502622 Simplifying x + 8 = -5.291502622 Reorder the terms: 8 + x = -5.291502622 Solving 8 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.291502622 + -8 x = -5.291502622 + -8 Combine like terms: -5.291502622 + -8 = -13.291502622 x = -13.291502622 Simplifying x = -13.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.708497378, -13.291502622}Solution
x = {0, -2.708497378, -13.291502622}
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