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Simplifying x4 + -19x2 + -90 = 0 Reorder the terms: -90 + -19x2 + x4 = 0 Solving -90 + -19x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -19x2 + 90 + x4 = 0 + 90 Reorder the terms: -90 + 90 + -19x2 + x4 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -19x2 + x4 = 0 + 90 -19x2 + x4 = 0 + 90 Combine like terms: 0 + 90 = 90 -19x2 + x4 = 90 The x term is -19x2. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x2 + 90.25 + x4 = 90 + 90.25 Reorder the terms: 90.25 + -19x2 + x4 = 90 + 90.25 Combine like terms: 90 + 90.25 = 180.25 90.25 + -19x2 + x4 = 180.25 Factor a perfect square on the left side: (x2 + -9.5)(x2 + -9.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x2 + -9.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x2 + -9.5 = 13.425721582 Simplifying x2 + -9.5 = 13.425721582 Reorder the terms: -9.5 + x2 = 13.425721582 Solving -9.5 + x2 = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x2 = 13.425721582 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x2 = 13.425721582 + 9.5 x2 = 13.425721582 + 9.5 Combine like terms: 13.425721582 + 9.5 = 22.925721582 x2 = 22.925721582 Simplifying x2 = 22.925721582 Take the square root of each side: x = {-4.7880812, 4.7880812}Subproblem 2
x2 + -9.5 = -13.425721582 Simplifying x2 + -9.5 = -13.425721582 Reorder the terms: -9.5 + x2 = -13.425721582 Solving -9.5 + x2 = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x2 = -13.425721582 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x2 = -13.425721582 + 9.5 x2 = -13.425721582 + 9.5 Combine like terms: -13.425721582 + 9.5 = -3.925721582 x2 = -3.925721582 Simplifying x2 = -3.925721582 Reorder the terms: 3.925721582 + x2 = -3.925721582 + 3.925721582 Combine like terms: -3.925721582 + 3.925721582 = 0.000000000 3.925721582 + 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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