x^4+17x^2+35=0

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Solution for x^4+17x^2+35=0 equation:


Simplifying
x4 + 17x2 + 35 = 0

Reorder the terms:
35 + 17x2 + x4 = 0

Solving
35 + 17x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 17x2 + -35 + x4 = 0 + -35

Reorder the terms:
35 + -35 + 17x2 + x4 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 17x2 + x4 = 0 + -35
17x2 + x4 = 0 + -35

Combine like terms: 0 + -35 = -35
17x2 + x4 = -35

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 = -35 + 72.25

Reorder the terms:
72.25 + 17x2 + x4 = -35 + 72.25

Combine like terms: -35 + 72.25 = 37.25
72.25 + 17x2 + x4 = 37.25

Factor a perfect square on the left side:
(x2 + 8.5)(x2 + 8.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x2 + 8.5) equal to 6.103277808 and -6.103277808.

Subproblem 1

x2 + 8.5 = 6.103277808 Simplifying x2 + 8.5 = 6.103277808 Reorder the terms: 8.5 + x2 = 6.103277808 Solving 8.5 + x2 = 6.103277808 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 = 6.103277808 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x2 = 6.103277808 + -8.5 x2 = 6.103277808 + -8.5 Combine like terms: 6.103277808 + -8.5 = -2.396722192 x2 = -2.396722192 Simplifying x2 = -2.396722192 Reorder the terms: 2.396722192 + x2 = -2.396722192 + 2.396722192 Combine like terms: -2.396722192 + 2.396722192 = 0.000000000 2.396722192 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x2 + 8.5 = -6.103277808 Simplifying x2 + 8.5 = -6.103277808 Reorder the terms: 8.5 + x2 = -6.103277808 Solving 8.5 + x2 = -6.103277808 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 = -6.103277808 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x2 = -6.103277808 + -8.5 x2 = -6.103277808 + -8.5 Combine like terms: -6.103277808 + -8.5 = -14.603277808 x2 = -14.603277808 Simplifying x2 = -14.603277808 Reorder the terms: 14.603277808 + x2 = -14.603277808 + 14.603277808 Combine like terms: -14.603277808 + 14.603277808 = 0.000000000 14.603277808 + 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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