(5x^4-3x^2+9)-(6x^4+11x^2-10)=

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Solution for (5x^4-3x^2+9)-(6x^4+11x^2-10)= equation:


Simplifying
(5x4 + -3x2 + 9) + -1(6x4 + 11x2 + -10) = 0

Reorder the terms:
(9 + -3x2 + 5x4) + -1(6x4 + 11x2 + -10) = 0

Remove parenthesis around (9 + -3x2 + 5x4)
9 + -3x2 + 5x4 + -1(6x4 + 11x2 + -10) = 0

Reorder the terms:
9 + -3x2 + 5x4 + -1(-10 + 11x2 + 6x4) = 0
9 + -3x2 + 5x4 + (-10 * -1 + 11x2 * -1 + 6x4 * -1) = 0
9 + -3x2 + 5x4 + (10 + -11x2 + -6x4) = 0

Reorder the terms:
9 + 10 + -3x2 + -11x2 + 5x4 + -6x4 = 0

Combine like terms: 9 + 10 = 19
19 + -3x2 + -11x2 + 5x4 + -6x4 = 0

Combine like terms: -3x2 + -11x2 = -14x2
19 + -14x2 + 5x4 + -6x4 = 0

Combine like terms: 5x4 + -6x4 = -1x4
19 + -14x2 + -1x4 = 0

Solving
19 + -14x2 + -1x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-19 + 14x2 + x4 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 14x2 + 19 + x4 = 0 + 19

Reorder the terms:
-19 + 19 + 14x2 + x4 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 14x2 + x4 = 0 + 19
14x2 + x4 = 0 + 19

Combine like terms: 0 + 19 = 19
14x2 + x4 = 19

The x term is 14x2.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x2 + 49 + x4 = 19 + 49

Reorder the terms:
49 + 14x2 + x4 = 19 + 49

Combine like terms: 19 + 49 = 68
49 + 14x2 + x4 = 68

Factor a perfect square on the left side:
(x2 + 7)(x2 + 7) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(x2 + 7) equal to 8.246211251 and -8.246211251.

Subproblem 1

x2 + 7 = 8.246211251 Simplifying x2 + 7 = 8.246211251 Reorder the terms: 7 + x2 = 8.246211251 Solving 7 + x2 = 8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x2 = 8.246211251 + -7 Combine like terms: 7 + -7 = 0 0 + x2 = 8.246211251 + -7 x2 = 8.246211251 + -7 Combine like terms: 8.246211251 + -7 = 1.246211251 x2 = 1.246211251 Simplifying x2 = 1.246211251 Take the square root of each side: x = {-1.116338323, 1.116338323}

Subproblem 2

x2 + 7 = -8.246211251 Simplifying x2 + 7 = -8.246211251 Reorder the terms: 7 + x2 = -8.246211251 Solving 7 + x2 = -8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x2 = -8.246211251 + -7 Combine like terms: 7 + -7 = 0 0 + x2 = -8.246211251 + -7 x2 = -8.246211251 + -7 Combine like terms: -8.246211251 + -7 = -15.246211251 x2 = -15.246211251 Simplifying x2 = -15.246211251 Reorder the terms: 15.246211251 + x2 = -15.246211251 + 15.246211251 Combine like terms: -15.246211251 + 15.246211251 = 0.000000000 15.246211251 + 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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