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Simplifying x4 + -4x2 + -24 = 0 Reorder the terms: -24 + -4x2 + x4 = 0 Solving -24 + -4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -4x2 + 24 + x4 = 0 + 24 Reorder the terms: -24 + 24 + -4x2 + x4 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4x2 + x4 = 0 + 24 -4x2 + x4 = 0 + 24 Combine like terms: 0 + 24 = 24 -4x2 + x4 = 24 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 = 24 + 4 Reorder the terms: 4 + -4x2 + x4 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + -4x2 + x4 = 28 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x2 + -2) equal to 5.291502622 and -5.291502622.Subproblem 1
x2 + -2 = 5.291502622 Simplifying x2 + -2 = 5.291502622 Reorder the terms: -2 + x2 = 5.291502622 Solving -2 + x2 = 5.291502622 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 = 5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 5.291502622 + 2 x2 = 5.291502622 + 2 Combine like terms: 5.291502622 + 2 = 7.291502622 x2 = 7.291502622 Simplifying x2 = 7.291502622 Take the square root of each side: x = {-2.700278249, 2.700278249}Subproblem 2
x2 + -2 = -5.291502622 Simplifying x2 + -2 = -5.291502622 Reorder the terms: -2 + x2 = -5.291502622 Solving -2 + x2 = -5.291502622 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 = -5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -5.291502622 + 2 x2 = -5.291502622 + 2 Combine like terms: -5.291502622 + 2 = -3.291502622 x2 = -3.291502622 Simplifying x2 = -3.291502622 Reorder the terms: 3.291502622 + x2 = -3.291502622 + 3.291502622 Combine like terms: -3.291502622 + 3.291502622 = 0.000000000 3.291502622 + 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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