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Simplifying x4 + -17x2 = 16 Reorder the terms: -17x2 + x4 = 16 Solving -17x2 + x4 = 16 Solving for variable 'x'. Reorder the terms: -16 + -17x2 + x4 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -17x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -17x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + -17x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -17x2 + x4 = 0 + 16 -17x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 -17x2 + x4 = 16 The x term is -17x2. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x2 + 72.25 + x4 = 16 + 72.25 Reorder the terms: 72.25 + -17x2 + x4 = 16 + 72.25 Combine like terms: 16 + 72.25 = 88.25 72.25 + -17x2 + x4 = 88.25 Factor a perfect square on the left side: (x2 + -8.5)(x2 + -8.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x2 + -8.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x2 + -8.5 = 9.394147114 Simplifying x2 + -8.5 = 9.394147114 Reorder the terms: -8.5 + x2 = 9.394147114 Solving -8.5 + x2 = 9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = 9.394147114 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = 9.394147114 + 8.5 x2 = 9.394147114 + 8.5 Combine like terms: 9.394147114 + 8.5 = 17.894147114 x2 = 17.894147114 Simplifying x2 = 17.894147114 Take the square root of each side: x = {-4.23014741, 4.23014741}Subproblem 2
x2 + -8.5 = -9.394147114 Simplifying x2 + -8.5 = -9.394147114 Reorder the terms: -8.5 + x2 = -9.394147114 Solving -8.5 + x2 = -9.394147114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = -9.394147114 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = -9.394147114 + 8.5 x2 = -9.394147114 + 8.5 Combine like terms: -9.394147114 + 8.5 = -0.894147114 x2 = -0.894147114 Simplifying x2 = -0.894147114 Reorder the terms: 0.894147114 + x2 = -0.894147114 + 0.894147114 Combine like terms: -0.894147114 + 0.894147114 = 0.000000000 0.894147114 + 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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