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Simplifying 2x3 + 22x2 + -104x = 0 Reorder the terms: -104x + 22x2 + 2x3 = 0 Solving -104x + 22x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-52 + 11x + x2) = 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 '(-52 + 11x + x2)' equal to zero and attempt to solve: Simplifying -52 + 11x + x2 = 0 Solving -52 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 11x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 11x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 11x + x2 = 0 + 52 11x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 11x + x2 = 52 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 52 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 52 + 30.25 Combine like terms: 52 + 30.25 = 82.25 30.25 + 11x + x2 = 82.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + 5.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + 5.5 = 9.069178574 Simplifying x + 5.5 = 9.069178574 Reorder the terms: 5.5 + x = 9.069178574 Solving 5.5 + x = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 9.069178574 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9.069178574 + -5.5 x = 9.069178574 + -5.5 Combine like terms: 9.069178574 + -5.5 = 3.569178574 x = 3.569178574 Simplifying x = 3.569178574Subproblem 2
x + 5.5 = -9.069178574 Simplifying x + 5.5 = -9.069178574 Reorder the terms: 5.5 + x = -9.069178574 Solving 5.5 + x = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -9.069178574 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9.069178574 + -5.5 x = -9.069178574 + -5.5 Combine like terms: -9.069178574 + -5.5 = -14.569178574 x = -14.569178574 Simplifying x = -14.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.569178574, -14.569178574}Solution
x = {0, 3.569178574, -14.569178574}
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