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Simplifying x4 + -3x2 + -72 = 0 Reorder the terms: -72 + -3x2 + x4 = 0 Solving -72 + -3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -3x2 + 72 + x4 = 0 + 72 Reorder the terms: -72 + 72 + -3x2 + x4 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -3x2 + x4 = 0 + 72 -3x2 + x4 = 0 + 72 Combine like terms: 0 + 72 = 72 -3x2 + x4 = 72 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 = 72 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 72 + 2.25 Combine like terms: 72 + 2.25 = 74.25 2.25 + -3x2 + x4 = 74.25 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x2 + -1.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x2 + -1.5 = 8.61684397 Simplifying x2 + -1.5 = 8.61684397 Reorder the terms: -1.5 + x2 = 8.61684397 Solving -1.5 + x2 = 8.61684397 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 = 8.61684397 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 8.61684397 + 1.5 x2 = 8.61684397 + 1.5 Combine like terms: 8.61684397 + 1.5 = 10.11684397 x2 = 10.11684397 Simplifying x2 = 10.11684397 Take the square root of each side: x = {-3.180698661, 3.180698661}Subproblem 2
x2 + -1.5 = -8.61684397 Simplifying x2 + -1.5 = -8.61684397 Reorder the terms: -1.5 + x2 = -8.61684397 Solving -1.5 + x2 = -8.61684397 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 = -8.61684397 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -8.61684397 + 1.5 x2 = -8.61684397 + 1.5 Combine like terms: -8.61684397 + 1.5 = -7.11684397 x2 = -7.11684397 Simplifying x2 = -7.11684397 Reorder the terms: 7.11684397 + x2 = -7.11684397 + 7.11684397 Combine like terms: -7.11684397 + 7.11684397 = 0.00000000 7.11684397 + x2 = 0.00000000 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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