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Simplifying x3 + 36x2 + 32x = 0 Reorder the terms: 32x + 36x2 + x3 = 0 Solving 32x + 36x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(32 + 36x + 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 '(32 + 36x + x2)' equal to zero and attempt to solve: Simplifying 32 + 36x + x2 = 0 Solving 32 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 36x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 36x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 36x + x2 = 0 + -32 36x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 36x + x2 = -32 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -32 + 324 Reorder the terms: 324 + 36x + x2 = -32 + 324 Combine like terms: -32 + 324 = 292 324 + 36x + x2 = 292 Factor a perfect square on the left side: (x + 18)(x + 18) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + 18) equal to 17.088007491 and -17.088007491.Subproblem 1
x + 18 = 17.088007491 Simplifying x + 18 = 17.088007491 Reorder the terms: 18 + x = 17.088007491 Solving 18 + x = 17.088007491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 17.088007491 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.088007491 + -18 x = 17.088007491 + -18 Combine like terms: 17.088007491 + -18 = -0.911992509 x = -0.911992509 Simplifying x = -0.911992509Subproblem 2
x + 18 = -17.088007491 Simplifying x + 18 = -17.088007491 Reorder the terms: 18 + x = -17.088007491 Solving 18 + x = -17.088007491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -17.088007491 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.088007491 + -18 x = -17.088007491 + -18 Combine like terms: -17.088007491 + -18 = -35.088007491 x = -35.088007491 Simplifying x = -35.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.911992509, -35.088007491}Solution
x = {0, -0.911992509, -35.088007491}
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