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Simplifying x4 + -4x2 = 42 Reorder the terms: -4x2 + x4 = 42 Solving -4x2 + x4 = 42 Solving for variable 'x'. Reorder the terms: -42 + -4x2 + x4 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -4x2 + 42 + x4 = 0 + 42 Reorder the terms: -42 + 42 + -4x2 + x4 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -4x2 + x4 = 0 + 42 -4x2 + x4 = 0 + 42 Combine like terms: 0 + 42 = 42 -4x2 + x4 = 42 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 = 42 + 4 Reorder the terms: 4 + -4x2 + x4 = 42 + 4 Combine like terms: 42 + 4 = 46 4 + -4x2 + x4 = 46 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x2 + -2) equal to 6.782329983 and -6.782329983.Subproblem 1
x2 + -2 = 6.782329983 Simplifying x2 + -2 = 6.782329983 Reorder the terms: -2 + x2 = 6.782329983 Solving -2 + x2 = 6.782329983 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 = 6.782329983 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 6.782329983 + 2 x2 = 6.782329983 + 2 Combine like terms: 6.782329983 + 2 = 8.782329983 x2 = 8.782329983 Simplifying x2 = 8.782329983 Take the square root of each side: x = {-2.963499618, 2.963499618}Subproblem 2
x2 + -2 = -6.782329983 Simplifying x2 + -2 = -6.782329983 Reorder the terms: -2 + x2 = -6.782329983 Solving -2 + x2 = -6.782329983 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 = -6.782329983 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -6.782329983 + 2 x2 = -6.782329983 + 2 Combine like terms: -6.782329983 + 2 = -4.782329983 x2 = -4.782329983 Simplifying x2 = -4.782329983 Reorder the terms: 4.782329983 + x2 = -4.782329983 + 4.782329983 Combine like terms: -4.782329983 + 4.782329983 = 0.000000000 4.782329983 + 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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