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Simplifying 0 = 2x3 + -6x2 + -32x Reorder the terms: 0 = -32x + -6x2 + 2x3 Solving 0 = -32x + -6x2 + 2x3 Solving for variable 'x'. Remove the zero: 32x + 6x2 + -2x3 = -32x + -6x2 + 2x3 + 32x + 6x2 + -2x3 Reorder the terms: 32x + 6x2 + -2x3 = -32x + 32x + -6x2 + 6x2 + 2x3 + -2x3 Combine like terms: -32x + 32x = 0 32x + 6x2 + -2x3 = 0 + -6x2 + 6x2 + 2x3 + -2x3 32x + 6x2 + -2x3 = -6x2 + 6x2 + 2x3 + -2x3 Combine like terms: -6x2 + 6x2 = 0 32x + 6x2 + -2x3 = 0 + 2x3 + -2x3 32x + 6x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 32x + 6x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(16 + 3x + -1x2) = 0 Ignore the factor 2.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 '(16 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 16 + 3x + -1x2 = 0 Solving 16 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + -3x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -3x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -3x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -3x + x2 = 0 + 16 -3x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -3x + x2 = 16 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 16 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 16 + 2.25 Combine like terms: 16 + 2.25 = 18.25 2.25 + -3x + x2 = 18.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -1.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -1.5 = 4.272001873 Simplifying x + -1.5 = 4.272001873 Reorder the terms: -1.5 + x = 4.272001873 Solving -1.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 4.272001873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.272001873 + 1.5 x = 4.272001873 + 1.5 Combine like terms: 4.272001873 + 1.5 = 5.772001873 x = 5.772001873 Simplifying x = 5.772001873Subproblem 2
x + -1.5 = -4.272001873 Simplifying x + -1.5 = -4.272001873 Reorder the terms: -1.5 + x = -4.272001873 Solving -1.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -4.272001873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.272001873 + 1.5 x = -4.272001873 + 1.5 Combine like terms: -4.272001873 + 1.5 = -2.772001873 x = -2.772001873 Simplifying x = -2.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.772001873, -2.772001873}Solution
x = {0, 5.772001873, -2.772001873}
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