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Simplifying 32x3 + -33x + -6x2 = 0 Reorder the terms: -33x + -6x2 + 32x3 = 0 Solving -33x + -6x2 + 32x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-33 + -6x + 32x2) = 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 '(-33 + -6x + 32x2)' equal to zero and attempt to solve: Simplifying -33 + -6x + 32x2 = 0 Solving -33 + -6x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.03125 + -0.1875x + x2 = 0 Move the constant term to the right: Add '1.03125' to each side of the equation. -1.03125 + -0.1875x + 1.03125 + x2 = 0 + 1.03125 Reorder the terms: -1.03125 + 1.03125 + -0.1875x + x2 = 0 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + -0.1875x + x2 = 0 + 1.03125 -0.1875x + x2 = 0 + 1.03125 Combine like terms: 0 + 1.03125 = 1.03125 -0.1875x + x2 = 1.03125 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 1.03125 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 1.03125 + 0.0087890625 Combine like terms: 1.03125 + 0.0087890625 = 1.0400390625 0.0087890625 + -0.1875x + x2 = 1.0400390625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 1.0400390625 Calculate the square root of the right side: 1.019823055 Break this problem into two subproblems by setting (x + -0.09375) equal to 1.019823055 and -1.019823055.Subproblem 1
x + -0.09375 = 1.019823055 Simplifying x + -0.09375 = 1.019823055 Reorder the terms: -0.09375 + x = 1.019823055 Solving -0.09375 + x = 1.019823055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 1.019823055 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 1.019823055 + 0.09375 x = 1.019823055 + 0.09375 Combine like terms: 1.019823055 + 0.09375 = 1.113573055 x = 1.113573055 Simplifying x = 1.113573055Subproblem 2
x + -0.09375 = -1.019823055 Simplifying x + -0.09375 = -1.019823055 Reorder the terms: -0.09375 + x = -1.019823055 Solving -0.09375 + x = -1.019823055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -1.019823055 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -1.019823055 + 0.09375 x = -1.019823055 + 0.09375 Combine like terms: -1.019823055 + 0.09375 = -0.926073055 x = -0.926073055 Simplifying x = -0.926073055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.113573055, -0.926073055}Solution
x = {0, 1.113573055, -0.926073055}
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