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Simplifying 32x3 + -24x2 + -92x = 0 Reorder the terms: -92x + -24x2 + 32x3 = 0 Solving -92x + -24x2 + 32x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-23 + -6x + 8x2) = 0 Ignore the factor 4.Subproblem 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 '(-23 + -6x + 8x2)' equal to zero and attempt to solve: Simplifying -23 + -6x + 8x2 = 0 Solving -23 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + -0.75x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -0.75x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -0.75x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -0.75x + x2 = 0 + 2.875 -0.75x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -0.75x + x2 = 2.875 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 = 2.875 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 2.875 + 0.140625 Combine like terms: 2.875 + 0.140625 = 3.015625 0.140625 + -0.75x + x2 = 3.015625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + -0.375) equal to 1.736555499 and -1.736555499.Subproblem 1
x + -0.375 = 1.736555499 Simplifying x + -0.375 = 1.736555499 Reorder the terms: -0.375 + x = 1.736555499 Solving -0.375 + x = 1.736555499 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 = 1.736555499 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.736555499 + 0.375 x = 1.736555499 + 0.375 Combine like terms: 1.736555499 + 0.375 = 2.111555499 x = 2.111555499 Simplifying x = 2.111555499Subproblem 2
x + -0.375 = -1.736555499 Simplifying x + -0.375 = -1.736555499 Reorder the terms: -0.375 + x = -1.736555499 Solving -0.375 + x = -1.736555499 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 = -1.736555499 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.736555499 + 0.375 x = -1.736555499 + 0.375 Combine like terms: -1.736555499 + 0.375 = -1.361555499 x = -1.361555499 Simplifying x = -1.361555499Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.111555499, -1.361555499}Solution
x = {0, 2.111555499, -1.361555499}
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