7x^4+3x^2-11-(-5x^4)-8x^2+6=

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Solution for 7x^4+3x^2-11-(-5x^4)-8x^2+6= equation: 


Simplifying
7x4 + 3x2 + -11 + -1(-5x4) + -8x2 + 6 = 0

Remove parenthesis around (-5x4)
7x4 + 3x2 + -11 + -1 * -5x4 + -8x2 + 6 = 0

Multiply -1 * -5
7x4 + 3x2 + -11 + 5x4 + -8x2 + 6 = 0

Reorder the terms:
-11 + 6 + 3x2 + -8x2 + 7x4 + 5x4 = 0

Combine like terms: -11 + 6 = -5
-5 + 3x2 + -8x2 + 7x4 + 5x4 = 0

Combine like terms: 3x2 + -8x2 = -5x2
-5 + -5x2 + 7x4 + 5x4 = 0

Combine like terms: 7x4 + 5x4 = 12x4
-5 + -5x2 + 12x4 = 0

Solving
-5 + -5x2 + 12x4 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-0.4166666667 + -0.4166666667x2 + x4 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -0.4166666667x2 + 0.4166666667 + x4 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -0.4166666667x2 + x4 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -0.4166666667x2 + x4 = 0 + 0.4166666667
-0.4166666667x2 + x4 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-0.4166666667x2 + x4 = 0.4166666667

The x term is -0.4166666667x2.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667x2 + 0.04340277781 + x4 = 0.4166666667 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667x2 + x4 = 0.4166666667 + 0.04340277781

Combine like terms: 0.4166666667 + 0.04340277781 = 0.46006944451
0.04340277781 + -0.4166666667x2 + x4 = 0.46006944451

Factor a perfect square on the left side:
(x2 + -0.2083333334)(x2 + -0.2083333334) = 0.46006944451

Calculate the square root of the right side: 0.678284192

Break this problem into two subproblems by setting 
(x2 + -0.2083333334) equal to 0.678284192 and -0.678284192.


Subproblem 1
x2 + -0.2083333334 = 0.678284192

Simplifying
x2 + -0.2083333334 = 0.678284192

Reorder the terms:
-0.2083333334 + x2 = 0.678284192

Solving
-0.2083333334 + x2 = 0.678284192

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x2 = 0.678284192 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x2 = 0.678284192 + 0.2083333334
x2 = 0.678284192 + 0.2083333334

Combine like terms: 0.678284192 + 0.2083333334 = 0.8866175254
x2 = 0.8866175254

Simplifying
x2 = 0.8866175254

Take the square root of each side:
x = {-0.941603699, 0.941603699}


Subproblem 2
x2 + -0.2083333334 = -0.678284192

Simplifying
x2 + -0.2083333334 = -0.678284192

Reorder the terms:
-0.2083333334 + x2 = -0.678284192

Solving
-0.2083333334 + x2 = -0.678284192

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + x2 = -0.678284192 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + x2 = -0.678284192 + 0.2083333334
x2 = -0.678284192 + 0.2083333334

Combine like terms: -0.678284192 + 0.2083333334 = -0.4699508586
x2 = -0.4699508586

Simplifying
x2 = -0.4699508586

Reorder the terms:
0.4699508586 + x2 = -0.4699508586 + 0.4699508586

Combine like terms: -0.4699508586 + 0.4699508586 = 0.0000000000
0.4699508586 + x2 = 0.0000000000

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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