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Simplifying 0 = -2x4 + 80x2 + 8 Reorder the terms: 0 = 8 + 80x2 + -2x4 Solving 0 = 8 + 80x2 + -2x4 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -80x2 + 2x4 = 8 + 80x2 + -2x4 + -8 + -80x2 + 2x4 Reorder the terms: -8 + -80x2 + 2x4 = 8 + -8 + 80x2 + -80x2 + -2x4 + 2x4 Combine like terms: 8 + -8 = 0 -8 + -80x2 + 2x4 = 0 + 80x2 + -80x2 + -2x4 + 2x4 -8 + -80x2 + 2x4 = 80x2 + -80x2 + -2x4 + 2x4 Combine like terms: 80x2 + -80x2 = 0 -8 + -80x2 + 2x4 = 0 + -2x4 + 2x4 -8 + -80x2 + 2x4 = -2x4 + 2x4 Combine like terms: -2x4 + 2x4 = 0 -8 + -80x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -40x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -40x2 + x4)' equal to zero and attempt to solve: Simplifying -4 + -40x2 + x4 = 0 Solving -4 + -40x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -40x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + -40x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -40x2 + x4 = 0 + 4 -40x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -40x2 + x4 = 4 The x term is -40x2. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x2 + 400 + x4 = 4 + 400 Reorder the terms: 400 + -40x2 + x4 = 4 + 400 Combine like terms: 4 + 400 = 404 400 + -40x2 + x4 = 404 Factor a perfect square on the left side: (x2 + -20)(x2 + -20) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x2 + -20) equal to 20.099751242 and -20.099751242.Subproblem 1
x2 + -20 = 20.099751242 Simplifying x2 + -20 = 20.099751242 Reorder the terms: -20 + x2 = 20.099751242 Solving -20 + x2 = 20.099751242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x2 = 20.099751242 + 20 Combine like terms: -20 + 20 = 0 0 + x2 = 20.099751242 + 20 x2 = 20.099751242 + 20 Combine like terms: 20.099751242 + 20 = 40.099751242 x2 = 40.099751242 Simplifying x2 = 40.099751242 Take the square root of each side: x = {-6.332436438, 6.332436438}Subproblem 2
x2 + -20 = -20.099751242 Simplifying x2 + -20 = -20.099751242 Reorder the terms: -20 + x2 = -20.099751242 Solving -20 + x2 = -20.099751242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x2 = -20.099751242 + 20 Combine like terms: -20 + 20 = 0 0 + x2 = -20.099751242 + 20 x2 = -20.099751242 + 20 Combine like terms: -20.099751242 + 20 = -0.099751242 x2 = -0.099751242 Simplifying x2 = -0.099751242 Reorder the terms: 0.099751242 + x2 = -0.099751242 + 0.099751242 Combine like terms: -0.099751242 + 0.099751242 = 0.000000000 0.099751242 + 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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