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Simplifying x4 + -3x2 + -5 = 0 Reorder the terms: -5 + -3x2 + x4 = 0 Solving -5 + -3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -3x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + -3x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x2 + x4 = 0 + 5 -3x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 -3x2 + x4 = 5 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 = 5 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + -3x2 + x4 = 7.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x2 + -1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x2 + -1.5 = 2.692582404 Simplifying x2 + -1.5 = 2.692582404 Reorder the terms: -1.5 + x2 = 2.692582404 Solving -1.5 + x2 = 2.692582404 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 = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 2.692582404 + 1.5 x2 = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 x2 = 4.192582404 Simplifying x2 = 4.192582404 Take the square root of each side: x = {-2.047579645, 2.047579645}Subproblem 2
x2 + -1.5 = -2.692582404 Simplifying x2 + -1.5 = -2.692582404 Reorder the terms: -1.5 + x2 = -2.692582404 Solving -1.5 + x2 = -2.692582404 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 = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -2.692582404 + 1.5 x2 = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 x2 = -1.192582404 Simplifying x2 = -1.192582404 Reorder the terms: 1.192582404 + x2 = -1.192582404 + 1.192582404 Combine like terms: -1.192582404 + 1.192582404 = 0.000000000 1.192582404 + 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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