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Simplifying x3 + 6x2 + -36x = 0 Reorder the terms: -36x + 6x2 + x3 = 0 Solving -36x + 6x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + 6x + 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 + 6x + x2)' equal to zero and attempt to solve: Simplifying -36 + 6x + x2 = 0 Solving -36 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6x + x2 = 0 + 36 6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 6x + x2 = 36 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 36 + 9 Reorder the terms: 9 + 6x + x2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6x + x2 = 45 Factor a perfect square on the left side: (x + 3)(x + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 3 = 6.708203933 Simplifying x + 3 = 6.708203933 Reorder the terms: 3 + x = 6.708203933 Solving 3 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.708203933 + -3 x = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 x = 3.708203933 Simplifying x = 3.708203933Subproblem 2
x + 3 = -6.708203933 Simplifying x + 3 = -6.708203933 Reorder the terms: 3 + x = -6.708203933 Solving 3 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.708203933 + -3 x = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 x = -9.708203933 Simplifying x = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.708203933, -9.708203933}Solution
x = {0, 3.708203933, -9.708203933}
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