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Simplifying x4 + -4x2 = 400 Reorder the terms: -4x2 + x4 = 400 Solving -4x2 + x4 = 400 Solving for variable 'x'. Reorder the terms: -400 + -4x2 + x4 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + -4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -4x2 + 400 + x4 = 0 + 400 Reorder the terms: -400 + 400 + -4x2 + x4 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -4x2 + x4 = 0 + 400 -4x2 + x4 = 0 + 400 Combine like terms: 0 + 400 = 400 -4x2 + x4 = 400 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 = 400 + 4 Reorder the terms: 4 + -4x2 + x4 = 400 + 4 Combine like terms: 400 + 4 = 404 4 + -4x2 + x4 = 404 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x2 + -2) equal to 20.099751242 and -20.099751242.Subproblem 1
x2 + -2 = 20.099751242 Simplifying x2 + -2 = 20.099751242 Reorder the terms: -2 + x2 = 20.099751242 Solving -2 + x2 = 20.099751242 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 = 20.099751242 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 20.099751242 + 2 x2 = 20.099751242 + 2 Combine like terms: 20.099751242 + 2 = 22.099751242 x2 = 22.099751242 Simplifying x2 = 22.099751242 Take the square root of each side: x = {-4.701037252, 4.701037252}Subproblem 2
x2 + -2 = -20.099751242 Simplifying x2 + -2 = -20.099751242 Reorder the terms: -2 + x2 = -20.099751242 Solving -2 + x2 = -20.099751242 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 = -20.099751242 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -20.099751242 + 2 x2 = -20.099751242 + 2 Combine like terms: -20.099751242 + 2 = -18.099751242 x2 = -18.099751242 Simplifying x2 = -18.099751242 Reorder the terms: 18.099751242 + x2 = -18.099751242 + 18.099751242 Combine like terms: -18.099751242 + 18.099751242 = 0.000000000 18.099751242 + 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.
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