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Simplifying 4x4 + 40x2 + 44 = 0 Reorder the terms: 44 + 40x2 + 4x4 = 0 Solving 44 + 40x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(11 + 10x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + 10x2 + x4)' equal to zero and attempt to solve: Simplifying 11 + 10x2 + x4 = 0 Solving 11 + 10x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 10x2 + -11 + x4 = 0 + -11 Reorder the terms: 11 + -11 + 10x2 + x4 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 10x2 + x4 = 0 + -11 10x2 + x4 = 0 + -11 Combine like terms: 0 + -11 = -11 10x2 + x4 = -11 The x term is 10x2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x2 + 25 + x4 = -11 + 25 Reorder the terms: 25 + 10x2 + x4 = -11 + 25 Combine like terms: -11 + 25 = 14 25 + 10x2 + x4 = 14 Factor a perfect square on the left side: (x2 + 5)(x2 + 5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x2 + 5) equal to 3.741657387 and -3.741657387.Subproblem 1
x2 + 5 = 3.741657387 Simplifying x2 + 5 = 3.741657387 Reorder the terms: 5 + x2 = 3.741657387 Solving 5 + x2 = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 3.741657387 + -5 x2 = 3.741657387 + -5 Combine like terms: 3.741657387 + -5 = -1.258342613 x2 = -1.258342613 Simplifying x2 = -1.258342613 Reorder the terms: 1.258342613 + x2 = -1.258342613 + 1.258342613 Combine like terms: -1.258342613 + 1.258342613 = 0.000000000 1.258342613 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 5 = -3.741657387 Simplifying x2 + 5 = -3.741657387 Reorder the terms: 5 + x2 = -3.741657387 Solving 5 + x2 = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = -3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = -3.741657387 + -5 x2 = -3.741657387 + -5 Combine like terms: -3.741657387 + -5 = -8.741657387 x2 = -8.741657387 Simplifying x2 = -8.741657387 Reorder the terms: 8.741657387 + x2 = -8.741657387 + 8.741657387 Combine like terms: -8.741657387 + 8.741657387 = 0.000000000 8.741657387 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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