x^4+5x^2-17=0

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Solution for x^4+5x^2-17=0 equation:


Simplifying
x4 + 5x2 + -17 = 0

Reorder the terms:
-17 + 5x2 + x4 = 0

Solving
-17 + 5x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 5x2 + 17 + x4 = 0 + 17

Reorder the terms:
-17 + 17 + 5x2 + x4 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 5x2 + x4 = 0 + 17
5x2 + x4 = 0 + 17

Combine like terms: 0 + 17 = 17
5x2 + x4 = 17

The x term is 5x2.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x2 + 6.25 + x4 = 17 + 6.25

Reorder the terms:
6.25 + 5x2 + x4 = 17 + 6.25

Combine like terms: 17 + 6.25 = 23.25
6.25 + 5x2 + x4 = 23.25

Factor a perfect square on the left side:
(x2 + 2.5)(x2 + 2.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x2 + 2.5) equal to 4.82182538 and -4.82182538.

Subproblem 1

x2 + 2.5 = 4.82182538 Simplifying x2 + 2.5 = 4.82182538 Reorder the terms: 2.5 + x2 = 4.82182538 Solving 2.5 + x2 = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 4.82182538 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 4.82182538 + -2.5 x2 = 4.82182538 + -2.5 Combine like terms: 4.82182538 + -2.5 = 2.32182538 x2 = 2.32182538 Simplifying x2 = 2.32182538 Take the square root of each side: x = {-1.523753714, 1.523753714}

Subproblem 2

x2 + 2.5 = -4.82182538 Simplifying x2 + 2.5 = -4.82182538 Reorder the terms: 2.5 + x2 = -4.82182538 Solving 2.5 + x2 = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -4.82182538 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -4.82182538 + -2.5 x2 = -4.82182538 + -2.5 Combine like terms: -4.82182538 + -2.5 = -7.32182538 x2 = -7.32182538 Simplifying x2 = -7.32182538 Reorder the terms: 7.32182538 + x2 = -7.32182538 + 7.32182538 Combine like terms: -7.32182538 + 7.32182538 = 0.00000000 7.32182538 + 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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