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Simplifying 4x5 + -44x4 + 4x3 = 0 Reorder the terms: 4x3 + -44x4 + 4x5 = 0 Solving 4x3 + -44x4 + 4x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x3'. 4x3(1 + -11x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -11x + x2)' equal to zero and attempt to solve: Simplifying 1 + -11x + x2 = 0 Solving 1 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -11x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -11x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11x + x2 = 0 + -1 -11x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -11x + x2 = -1 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 = -1 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + -11x + x2 = 29.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -5.5 = 5.408326913 Simplifying x + -5.5 = 5.408326913 Reorder the terms: -5.5 + x = 5.408326913 Solving -5.5 + x = 5.408326913 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 = 5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.408326913 + 5.5 x = 5.408326913 + 5.5 Combine like terms: 5.408326913 + 5.5 = 10.908326913 x = 10.908326913 Simplifying x = 10.908326913Subproblem 2
x + -5.5 = -5.408326913 Simplifying x + -5.5 = -5.408326913 Reorder the terms: -5.5 + x = -5.408326913 Solving -5.5 + x = -5.408326913 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 = -5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.408326913 + 5.5 x = -5.408326913 + 5.5 Combine like terms: -5.408326913 + 5.5 = 0.091673087 x = 0.091673087 Simplifying x = 0.091673087Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.908326913, 0.091673087}Solution
x = {10.908326913, 0.091673087}
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