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Simplifying x4 + -9x2 + -20 = 0 Reorder the terms: -20 + -9x2 + x4 = 0 Solving -20 + -9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -9x2 + 20 + x4 = 0 + 20 Reorder the terms: -20 + 20 + -9x2 + x4 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -9x2 + x4 = 0 + 20 -9x2 + x4 = 0 + 20 Combine like terms: 0 + 20 = 20 -9x2 + x4 = 20 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 = 20 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = 20 + 20.25 Combine like terms: 20 + 20.25 = 40.25 20.25 + -9x2 + x4 = 40.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x2 + -4.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x2 + -4.5 = 6.34428877 Simplifying x2 + -4.5 = 6.34428877 Reorder the terms: -4.5 + x2 = 6.34428877 Solving -4.5 + x2 = 6.34428877 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 = 6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 6.34428877 + 4.5 x2 = 6.34428877 + 4.5 Combine like terms: 6.34428877 + 4.5 = 10.84428877 x2 = 10.84428877 Simplifying x2 = 10.84428877 Take the square root of each side: x = {-3.293066773, 3.293066773}Subproblem 2
x2 + -4.5 = -6.34428877 Simplifying x2 + -4.5 = -6.34428877 Reorder the terms: -4.5 + x2 = -6.34428877 Solving -4.5 + x2 = -6.34428877 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 = -6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -6.34428877 + 4.5 x2 = -6.34428877 + 4.5 Combine like terms: -6.34428877 + 4.5 = -1.84428877 x2 = -1.84428877 Simplifying x2 = -1.84428877 Reorder the terms: 1.84428877 + x2 = -1.84428877 + 1.84428877 Combine like terms: -1.84428877 + 1.84428877 = 0.00000000 1.84428877 + 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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