9x^4=37x^2+4

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Solution for 9x^4=37x^2+4 equation:


Simplifying
9x4 = 37x2 + 4

Reorder the terms:
9x4 = 4 + 37x2

Solving
9x4 = 4 + 37x2

Solving for variable 'x'.

Reorder the terms:
-4 + -37x2 + 9x4 = 4 + 37x2 + -4 + -37x2

Reorder the terms:
-4 + -37x2 + 9x4 = 4 + -4 + 37x2 + -37x2

Combine like terms: 4 + -4 = 0
-4 + -37x2 + 9x4 = 0 + 37x2 + -37x2
-4 + -37x2 + 9x4 = 37x2 + -37x2

Combine like terms: 37x2 + -37x2 = 0
-4 + -37x2 + 9x4 = 0

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

Divide each side by '9'.
-0.4444444444 + -4.111111111x2 + x4 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -4.111111111x2 + 0.4444444444 + x4 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -4.111111111x2 + x4 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -4.111111111x2 + x4 = 0 + 0.4444444444
-4.111111111x2 + x4 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-4.111111111x2 + x4 = 0.4444444444

The x term is -4.111111111x2.  Take half its coefficient (-2.055555556).
Square it (4.225308644) and add it to both sides.

Add '4.225308644' to each side of the equation.
-4.111111111x2 + 4.225308644 + x4 = 0.4444444444 + 4.225308644

Reorder the terms:
4.225308644 + -4.111111111x2 + x4 = 0.4444444444 + 4.225308644

Combine like terms: 0.4444444444 + 4.225308644 = 4.6697530884
4.225308644 + -4.111111111x2 + x4 = 4.6697530884

Factor a perfect square on the left side:
(x2 + -2.055555556)(x2 + -2.055555556) = 4.6697530884

Calculate the square root of the right side: 2.160961149

Break this problem into two subproblems by setting 
(x2 + -2.055555556) equal to 2.160961149 and -2.160961149.

Subproblem 1

x2 + -2.055555556 = 2.160961149 Simplifying x2 + -2.055555556 = 2.160961149 Reorder the terms: -2.055555556 + x2 = 2.160961149 Solving -2.055555556 + x2 = 2.160961149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + x2 = 2.160961149 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = 2.160961149 + 2.055555556 x2 = 2.160961149 + 2.055555556 Combine like terms: 2.160961149 + 2.055555556 = 4.216516705 x2 = 4.216516705 Simplifying x2 = 4.216516705 Take the square root of each side: x = {-2.053415863, 2.053415863}

Subproblem 2

x2 + -2.055555556 = -2.160961149 Simplifying x2 + -2.055555556 = -2.160961149 Reorder the terms: -2.055555556 + x2 = -2.160961149 Solving -2.055555556 + x2 = -2.160961149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.055555556' to each side of the equation. -2.055555556 + 2.055555556 + x2 = -2.160961149 + 2.055555556 Combine like terms: -2.055555556 + 2.055555556 = 0.000000000 0.000000000 + x2 = -2.160961149 + 2.055555556 x2 = -2.160961149 + 2.055555556 Combine like terms: -2.160961149 + 2.055555556 = -0.105405593 x2 = -0.105405593 Simplifying x2 = -0.105405593 Reorder the terms: 0.105405593 + x2 = -0.105405593 + 0.105405593 Combine like terms: -0.105405593 + 0.105405593 = 0.000000000 0.105405593 + 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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