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Simplifying 2x3 + -21x2 + -108x = 0 Reorder the terms: -108x + -21x2 + 2x3 = 0 Solving -108x + -21x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-108 + -21x + 2x2) = 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 '(-108 + -21x + 2x2)' equal to zero and attempt to solve: Simplifying -108 + -21x + 2x2 = 0 Solving -108 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -54 + -10.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -10.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -10.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -10.5x + x2 = 0 + 54 -10.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -10.5x + x2 = 54 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 54 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 54 + 27.5625 Combine like terms: 54 + 27.5625 = 81.5625 27.5625 + -10.5x + x2 = 81.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 81.5625 Calculate the square root of the right side: 9.031195934 Break this problem into two subproblems by setting (x + -5.25) equal to 9.031195934 and -9.031195934.Subproblem 1
x + -5.25 = 9.031195934 Simplifying x + -5.25 = 9.031195934 Reorder the terms: -5.25 + x = 9.031195934 Solving -5.25 + x = 9.031195934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 9.031195934 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 9.031195934 + 5.25 x = 9.031195934 + 5.25 Combine like terms: 9.031195934 + 5.25 = 14.281195934 x = 14.281195934 Simplifying x = 14.281195934Subproblem 2
x + -5.25 = -9.031195934 Simplifying x + -5.25 = -9.031195934 Reorder the terms: -5.25 + x = -9.031195934 Solving -5.25 + x = -9.031195934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -9.031195934 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -9.031195934 + 5.25 x = -9.031195934 + 5.25 Combine like terms: -9.031195934 + 5.25 = -3.781195934 x = -3.781195934 Simplifying x = -3.781195934Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.281195934, -3.781195934}Solution
x = {0, 14.281195934, -3.781195934}
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