3x^4+11x^2-10=0

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Solution for 3x^4+11x^2-10=0 equation:


Simplifying
3x4 + 11x2 + -10 = 0

Reorder the terms:
-10 + 11x2 + 3x4 = 0

Solving
-10 + 11x2 + 3x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.333333333 + 3.666666667x2 + x4 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 3.666666667x2 + 3.333333333 + x4 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 3.666666667x2 + x4 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 3.666666667x2 + x4 = 0 + 3.333333333
3.666666667x2 + x4 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
3.666666667x2 + x4 = 3.333333333

The x term is 3.666666667x2.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x2 + 3.361111114 + x4 = 3.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x2 + x4 = 3.333333333 + 3.361111114

Combine like terms: 3.333333333 + 3.361111114 = 6.694444447
3.361111114 + 3.666666667x2 + x4 = 6.694444447

Factor a perfect square on the left side:
(x2 + 1.833333334)(x2 + 1.833333334) = 6.694444447

Calculate the square root of the right side: 2.58736245

Break this problem into two subproblems by setting 
(x2 + 1.833333334) equal to 2.58736245 and -2.58736245.

Subproblem 1

x2 + 1.833333334 = 2.58736245 Simplifying x2 + 1.833333334 = 2.58736245 Reorder the terms: 1.833333334 + x2 = 2.58736245 Solving 1.833333334 + x2 = 2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x2 = 2.58736245 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x2 = 2.58736245 + -1.833333334 x2 = 2.58736245 + -1.833333334 Combine like terms: 2.58736245 + -1.833333334 = 0.754029116 x2 = 0.754029116 Simplifying x2 = 0.754029116 Take the square root of each side: x = {-0.868348499, 0.868348499}

Subproblem 2

x2 + 1.833333334 = -2.58736245 Simplifying x2 + 1.833333334 = -2.58736245 Reorder the terms: 1.833333334 + x2 = -2.58736245 Solving 1.833333334 + x2 = -2.58736245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x2 = -2.58736245 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x2 = -2.58736245 + -1.833333334 x2 = -2.58736245 + -1.833333334 Combine like terms: -2.58736245 + -1.833333334 = -4.420695784 x2 = -4.420695784 Simplifying x2 = -4.420695784 Reorder the terms: 4.420695784 + x2 = -4.420695784 + 4.420695784 Combine like terms: -4.420695784 + 4.420695784 = 0.000000000 4.420695784 + 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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