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Simplifying (4x3) + (33x2) + 36x = 0 Reorder the terms: 36x + (33x2) + (4x3) = 0 Solving 36x + (33x2) + (4x3) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(36 + (33x) + (4x2)) = 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 + (33x) + (4x2))' equal to zero and attempt to solve: Simplifying 36 + (33x) + (4x2) = 0 Solving 36 + (33x) + (4x2) = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + (8.25x) + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + (8.25x) + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + (8.25x) + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + (8.25x) + x2 = 0 + -9 (8.25x) + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 (8.25x) + x2 = -9 The x term is (8.25x). Take half its coefficient (4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. (8.25x) + 17.015625 + x2 = -9 + 17.015625 Reorder the terms: 17.015625 + (8.25x) + x2 = -9 + 17.015625 Combine like terms: -9 + 17.015625 = 8.015625 17.015625 + (8.25x) + x2 = 8.015625 Factor a perfect square on the left side: ((x) + 4.125)((x) + 4.125) = 8.015625 Calculate the square root of the right side: 2.831187913 Break this problem into two subproblems by setting ((x) + 4.125) equal to 2.831187913 and -2.831187913.Subproblem 1
(x) + 4.125 = 2.831187913 Simplifying (x) + 4.125 = 2.831187913 x + 4.125 = 2.831187913 Reorder the terms: 4.125 + x = 2.831187913 Solving 4.125 + x = 2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = 2.831187913 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = 2.831187913 + -4.125 x = 2.831187913 + -4.125 Combine like terms: 2.831187913 + -4.125 = -1.293812087 x = -1.293812087 Simplifying x = -1.293812087Subproblem 2
(x) + 4.125 = -2.831187913 Simplifying (x) + 4.125 = -2.831187913 x + 4.125 = -2.831187913 Reorder the terms: 4.125 + x = -2.831187913 Solving 4.125 + x = -2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = -2.831187913 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = -2.831187913 + -4.125 x = -2.831187913 + -4.125 Combine like terms: -2.831187913 + -4.125 = -6.956187913 x = -6.956187913 Simplifying x = -6.956187913Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.293812087, -6.956187913}Solution
x = {0, -1.293812087, -6.956187913}
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