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Simplifying 2x4 + 8x2 + -20 = 0 Reorder the terms: -20 + 8x2 + 2x4 = 0 Solving -20 + 8x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 4x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying -10 + 4x2 + x4 = 0 Solving -10 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 4x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + 4x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4x2 + x4 = 0 + 10 4x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 4x2 + x4 = 10 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 10 + 4 Reorder the terms: 4 + 4x2 + x4 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + 4x2 + x4 = 14 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x2 + 2) equal to 3.741657387 and -3.741657387.Subproblem 1
x2 + 2 = 3.741657387 Simplifying x2 + 2 = 3.741657387 Reorder the terms: 2 + x2 = 3.741657387 Solving 2 + x2 = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 3.741657387 + -2 x2 = 3.741657387 + -2 Combine like terms: 3.741657387 + -2 = 1.741657387 x2 = 1.741657387 Simplifying x2 = 1.741657387 Take the square root of each side: x = {-1.319718677, 1.319718677}Subproblem 2
x2 + 2 = -3.741657387 Simplifying x2 + 2 = -3.741657387 Reorder the terms: 2 + x2 = -3.741657387 Solving 2 + x2 = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -3.741657387 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -3.741657387 + -2 x2 = -3.741657387 + -2 Combine like terms: -3.741657387 + -2 = -5.741657387 x2 = -5.741657387 Simplifying x2 = -5.741657387 Reorder the terms: 5.741657387 + x2 = -5.741657387 + 5.741657387 Combine like terms: -5.741657387 + 5.741657387 = 0.000000000 5.741657387 + 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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