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Simplifying X4 + -9X2 + -81 = 0 Reorder the terms: -81 + -9X2 + X4 = 0 Solving -81 + -9X2 + X4 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -9X2 + 81 + X4 = 0 + 81 Reorder the terms: -81 + 81 + -9X2 + X4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -9X2 + X4 = 0 + 81 -9X2 + X4 = 0 + 81 Combine like terms: 0 + 81 = 81 -9X2 + X4 = 81 The X term is -9X2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9X2 + 20.25 + X4 = 81 + 20.25 Reorder the terms: 20.25 + -9X2 + X4 = 81 + 20.25 Combine like terms: 81 + 20.25 = 101.25 20.25 + -9X2 + X4 = 101.25 Factor a perfect square on the left side: (X2 + -4.5)(X2 + -4.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (X2 + -4.5) equal to 10.062305899 and -10.062305899.Subproblem 1
X2 + -4.5 = 10.062305899 Simplifying X2 + -4.5 = 10.062305899 Reorder the terms: -4.5 + X2 = 10.062305899 Solving -4.5 + X2 = 10.062305899 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + X2 = 10.062305899 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X2 = 10.062305899 + 4.5 X2 = 10.062305899 + 4.5 Combine like terms: 10.062305899 + 4.5 = 14.562305899 X2 = 14.562305899 Simplifying X2 = 14.562305899 Take the square root of each side: X = {-3.816058949, 3.816058949}Subproblem 2
X2 + -4.5 = -10.062305899 Simplifying X2 + -4.5 = -10.062305899 Reorder the terms: -4.5 + X2 = -10.062305899 Solving -4.5 + X2 = -10.062305899 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + X2 = -10.062305899 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X2 = -10.062305899 + 4.5 X2 = -10.062305899 + 4.5 Combine like terms: -10.062305899 + 4.5 = -5.562305899 X2 = -5.562305899 Simplifying X2 = -5.562305899 Reorder the terms: 5.562305899 + X2 = -5.562305899 + 5.562305899 Combine like terms: -5.562305899 + 5.562305899 = 0.000000000 5.562305899 + 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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