4x^4-36x^2+9=0

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Solution for 4x^4-36x^2+9=0 equation:


Simplifying
4x4 + -36x2 + 9 = 0

Reorder the terms:
9 + -36x2 + 4x4 = 0

Solving
9 + -36x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
2.25 + -9x2 + x4 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -9x2 + -2.25 + x4 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -9x2 + x4 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -9x2 + x4 = 0 + -2.25
-9x2 + x4 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-9x2 + x4 = -2.25

The x term is -9x2.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x2 + 20.25 + x4 = -2.25 + 20.25

Reorder the terms:
20.25 + -9x2 + x4 = -2.25 + 20.25

Combine like terms: -2.25 + 20.25 = 18
20.25 + -9x2 + x4 = 18

Factor a perfect square on the left side:
(x2 + -4.5)(x2 + -4.5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x2 + -4.5) equal to 4.242640687 and -4.242640687.

Subproblem 1

x2 + -4.5 = 4.242640687 Simplifying x2 + -4.5 = 4.242640687 Reorder the terms: -4.5 + x2 = 4.242640687 Solving -4.5 + x2 = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 4.242640687 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 4.242640687 + 4.5 x2 = 4.242640687 + 4.5 Combine like terms: 4.242640687 + 4.5 = 8.742640687 x2 = 8.742640687 Simplifying x2 = 8.742640687 Take the square root of each side: x = {-2.956795679, 2.956795679}

Subproblem 2

x2 + -4.5 = -4.242640687 Simplifying x2 + -4.5 = -4.242640687 Reorder the terms: -4.5 + x2 = -4.242640687 Solving -4.5 + x2 = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -4.242640687 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -4.242640687 + 4.5 x2 = -4.242640687 + 4.5 Combine like terms: -4.242640687 + 4.5 = 0.257359313 x2 = 0.257359313 Simplifying x2 = 0.257359313 Take the square root of each side: x = {-0.507305936, 0.507305936}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.956795679, 2.956795679, -0.507305936, 0.507305936}

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