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Simplifying x4 + -5x2 + -16 = 0 Reorder the terms: -16 + -5x2 + x4 = 0 Solving -16 + -5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -5x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + -5x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5x2 + x4 = 0 + 16 -5x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 -5x2 + x4 = 16 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = 16 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 16 + 6.25 Combine like terms: 16 + 6.25 = 22.25 6.25 + -5x2 + x4 = 22.25 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x2 + -2.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x2 + -2.5 = 4.716990566 Simplifying x2 + -2.5 = 4.716990566 Reorder the terms: -2.5 + x2 = 4.716990566 Solving -2.5 + x2 = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 4.716990566 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 4.716990566 + 2.5 x2 = 4.716990566 + 2.5 Combine like terms: 4.716990566 + 2.5 = 7.216990566 x2 = 7.216990566 Simplifying x2 = 7.216990566 Take the square root of each side: x = {-2.686445712, 2.686445712}Subproblem 2
x2 + -2.5 = -4.716990566 Simplifying x2 + -2.5 = -4.716990566 Reorder the terms: -2.5 + x2 = -4.716990566 Solving -2.5 + x2 = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -4.716990566 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -4.716990566 + 2.5 x2 = -4.716990566 + 2.5 Combine like terms: -4.716990566 + 2.5 = -2.216990566 x2 = -2.216990566 Simplifying x2 = -2.216990566 Reorder the terms: 2.216990566 + x2 = -2.216990566 + 2.216990566 Combine like terms: -2.216990566 + 2.216990566 = 0.000000000 2.216990566 + 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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