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Simplifying x4 + -13x2 + -40 = 0 Reorder the terms: -40 + -13x2 + x4 = 0 Solving -40 + -13x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -13x2 + 40 + x4 = 0 + 40 Reorder the terms: -40 + 40 + -13x2 + x4 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -13x2 + x4 = 0 + 40 -13x2 + x4 = 0 + 40 Combine like terms: 0 + 40 = 40 -13x2 + x4 = 40 The x term is -13x2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x2 + 42.25 + x4 = 40 + 42.25 Reorder the terms: 42.25 + -13x2 + x4 = 40 + 42.25 Combine like terms: 40 + 42.25 = 82.25 42.25 + -13x2 + x4 = 82.25 Factor a perfect square on the left side: (x2 + -6.5)(x2 + -6.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x2 + -6.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x2 + -6.5 = 9.069178574 Simplifying x2 + -6.5 = 9.069178574 Reorder the terms: -6.5 + x2 = 9.069178574 Solving -6.5 + x2 = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = 9.069178574 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = 9.069178574 + 6.5 x2 = 9.069178574 + 6.5 Combine like terms: 9.069178574 + 6.5 = 15.569178574 x2 = 15.569178574 Simplifying x2 = 15.569178574 Take the square root of each side: x = {-3.945779844, 3.945779844}Subproblem 2
x2 + -6.5 = -9.069178574 Simplifying x2 + -6.5 = -9.069178574 Reorder the terms: -6.5 + x2 = -9.069178574 Solving -6.5 + x2 = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x2 = -9.069178574 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x2 = -9.069178574 + 6.5 x2 = -9.069178574 + 6.5 Combine like terms: -9.069178574 + 6.5 = -2.569178574 x2 = -2.569178574 Simplifying x2 = -2.569178574 Reorder the terms: 2.569178574 + x2 = -2.569178574 + 2.569178574 Combine like terms: -2.569178574 + 2.569178574 = 0.000000000 2.569178574 + 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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