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Simplifying x4 + 3x2 + -30 = 0 Reorder the terms: -30 + 3x2 + x4 = 0 Solving -30 + 3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 3x2 + 30 + x4 = 0 + 30 Reorder the terms: -30 + 30 + 3x2 + x4 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 3x2 + x4 = 0 + 30 3x2 + x4 = 0 + 30 Combine like terms: 0 + 30 = 30 3x2 + x4 = 30 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 = 30 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + 3x2 + x4 = 32.25 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x2 + 1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x2 + 1.5 = 5.678908346 Simplifying x2 + 1.5 = 5.678908346 Reorder the terms: 1.5 + x2 = 5.678908346 Solving 1.5 + x2 = 5.678908346 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 = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 5.678908346 + -1.5 x2 = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 x2 = 4.178908346 Simplifying x2 = 4.178908346 Take the square root of each side: x = {-2.04423784, 2.04423784}Subproblem 2
x2 + 1.5 = -5.678908346 Simplifying x2 + 1.5 = -5.678908346 Reorder the terms: 1.5 + x2 = -5.678908346 Solving 1.5 + x2 = -5.678908346 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 = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -5.678908346 + -1.5 x2 = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 x2 = -7.178908346 Simplifying x2 = -7.178908346 Reorder the terms: 7.178908346 + x2 = -7.178908346 + 7.178908346 Combine like terms: -7.178908346 + 7.178908346 = 0.000000000 7.178908346 + 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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