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Simplifying x4 + -3x2 + -20 = 0 Reorder the terms: -20 + -3x2 + x4 = 0 Solving -20 + -3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -3x2 + 20 + x4 = 0 + 20 Reorder the terms: -20 + 20 + -3x2 + x4 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -3x2 + x4 = 0 + 20 -3x2 + x4 = 0 + 20 Combine like terms: 0 + 20 = 20 -3x2 + x4 = 20 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = 20 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 20 + 2.25 Combine like terms: 20 + 2.25 = 22.25 2.25 + -3x2 + x4 = 22.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x2 + -1.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x2 + -1.5 = 4.716990566 Simplifying x2 + -1.5 = 4.716990566 Reorder the terms: -1.5 + x2 = 4.716990566 Solving -1.5 + x2 = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 4.716990566 + 1.5 x2 = 4.716990566 + 1.5 Combine like terms: 4.716990566 + 1.5 = 6.216990566 x2 = 6.216990566 Simplifying x2 = 6.216990566 Take the square root of each side: x = {-2.493389373, 2.493389373}Subproblem 2
x2 + -1.5 = -4.716990566 Simplifying x2 + -1.5 = -4.716990566 Reorder the terms: -1.5 + x2 = -4.716990566 Solving -1.5 + x2 = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -4.716990566 + 1.5 x2 = -4.716990566 + 1.5 Combine like terms: -4.716990566 + 1.5 = -3.216990566 x2 = -3.216990566 Simplifying x2 = -3.216990566 Reorder the terms: 3.216990566 + x2 = -3.216990566 + 3.216990566 Combine like terms: -3.216990566 + 3.216990566 = 0.000000000 3.216990566 + 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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