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Simplifying x4 + 11x3 + -8x2 = 0 Reorder the terms: -8x2 + 11x3 + x4 = 0 Solving -8x2 + 11x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-8 + 11x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-8 + 11x + x2)' equal to zero and attempt to solve: Simplifying -8 + 11x + x2 = 0 Solving -8 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 11x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 11x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 11x + x2 = 0 + 8 11x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 11x + x2 = 8 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 = 8 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 8 + 30.25 Combine like terms: 8 + 30.25 = 38.25 30.25 + 11x + x2 = 38.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + 5.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + 5.5 = 6.184658438 Simplifying x + 5.5 = 6.184658438 Reorder the terms: 5.5 + x = 6.184658438 Solving 5.5 + x = 6.184658438 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 = 6.184658438 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.184658438 + -5.5 x = 6.184658438 + -5.5 Combine like terms: 6.184658438 + -5.5 = 0.684658438 x = 0.684658438 Simplifying x = 0.684658438Subproblem 2
x + 5.5 = -6.184658438 Simplifying x + 5.5 = -6.184658438 Reorder the terms: 5.5 + x = -6.184658438 Solving 5.5 + x = -6.184658438 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 = -6.184658438 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.184658438 + -5.5 x = -6.184658438 + -5.5 Combine like terms: -6.184658438 + -5.5 = -11.684658438 x = -11.684658438 Simplifying x = -11.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.684658438, -11.684658438}Solution
x = {0, 0.684658438, -11.684658438}
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