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Simplifying 4x3 + -3x2 + -36x = 0 Reorder the terms: -36x + -3x2 + 4x3 = 0 Solving -36x + -3x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + -3x + 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 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying -36 + -3x + 4x2 = 0 Solving -36 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9 + -0.75x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.75x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.75x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.75x + x2 = 0 + 9 -0.75x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.75x + x2 = 9 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 9 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 9 + 0.140625 Combine like terms: 9 + 0.140625 = 9.140625 0.140625 + -0.75x + x2 = 9.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 9.140625 Calculate the square root of the right side: 3.023346656 Break this problem into two subproblems by setting (x + -0.375) equal to 3.023346656 and -3.023346656.Subproblem 1
x + -0.375 = 3.023346656 Simplifying x + -0.375 = 3.023346656 Reorder the terms: -0.375 + x = 3.023346656 Solving -0.375 + x = 3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 3.023346656 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 3.023346656 + 0.375 x = 3.023346656 + 0.375 Combine like terms: 3.023346656 + 0.375 = 3.398346656 x = 3.398346656 Simplifying x = 3.398346656Subproblem 2
x + -0.375 = -3.023346656 Simplifying x + -0.375 = -3.023346656 Reorder the terms: -0.375 + x = -3.023346656 Solving -0.375 + x = -3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -3.023346656 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -3.023346656 + 0.375 x = -3.023346656 + 0.375 Combine like terms: -3.023346656 + 0.375 = -2.648346656 x = -2.648346656 Simplifying x = -2.648346656Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.398346656, -2.648346656}Solution
x = {0, 3.398346656, -2.648346656}
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