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Simplifying x4 + -9x2 + -12 = 0 Reorder the terms: -12 + -9x2 + x4 = 0 Solving -12 + -9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -9x2 + 12 + x4 = 0 + 12 Reorder the terms: -12 + 12 + -9x2 + x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -9x2 + x4 = 0 + 12 -9x2 + x4 = 0 + 12 Combine like terms: 0 + 12 = 12 -9x2 + x4 = 12 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 = 12 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = 12 + 20.25 Combine like terms: 12 + 20.25 = 32.25 20.25 + -9x2 + x4 = 32.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x2 + -4.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x2 + -4.5 = 5.678908346 Simplifying x2 + -4.5 = 5.678908346 Reorder the terms: -4.5 + x2 = 5.678908346 Solving -4.5 + x2 = 5.678908346 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 = 5.678908346 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 5.678908346 + 4.5 x2 = 5.678908346 + 4.5 Combine like terms: 5.678908346 + 4.5 = 10.178908346 x2 = 10.178908346 Simplifying x2 = 10.178908346 Take the square root of each side: x = {-3.190440149, 3.190440149}Subproblem 2
x2 + -4.5 = -5.678908346 Simplifying x2 + -4.5 = -5.678908346 Reorder the terms: -4.5 + x2 = -5.678908346 Solving -4.5 + x2 = -5.678908346 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 = -5.678908346 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -5.678908346 + 4.5 x2 = -5.678908346 + 4.5 Combine like terms: -5.678908346 + 4.5 = -1.178908346 x2 = -1.178908346 Simplifying x2 = -1.178908346 Reorder the terms: 1.178908346 + x2 = -1.178908346 + 1.178908346 Combine like terms: -1.178908346 + 1.178908346 = 0.000000000 1.178908346 + 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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