4x^4-16x^2+9=0

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Solution for 4x^4-16x^2+9=0 equation:


Simplifying
4x4 + -16x2 + 9 = 0

Reorder the terms:
9 + -16x2 + 4x4 = 0

Solving
9 + -16x2 + 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 + -4x2 + x4 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -4x2 + -2.25 + x4 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -4x2 + x4 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -4x2 + x4 = 0 + -2.25
-4x2 + x4 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-4x2 + x4 = -2.25

The x term is -4x2.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x2 + 4 + x4 = -2.25 + 4

Reorder the terms:
4 + -4x2 + x4 = -2.25 + 4

Combine like terms: -2.25 + 4 = 1.75
4 + -4x2 + x4 = 1.75

Factor a perfect square on the left side:
(x2 + -2)(x2 + -2) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x2 + -2) equal to 1.322875656 and -1.322875656.

Subproblem 1

x2 + -2 = 1.322875656 Simplifying x2 + -2 = 1.322875656 Reorder the terms: -2 + x2 = 1.322875656 Solving -2 + x2 = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 1.322875656 + 2 x2 = 1.322875656 + 2 Combine like terms: 1.322875656 + 2 = 3.322875656 x2 = 3.322875656 Simplifying x2 = 3.322875656 Take the square root of each side: x = {-1.822875656, 1.822875656}

Subproblem 2

x2 + -2 = -1.322875656 Simplifying x2 + -2 = -1.322875656 Reorder the terms: -2 + x2 = -1.322875656 Solving -2 + x2 = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -1.322875656 + 2 x2 = -1.322875656 + 2 Combine like terms: -1.322875656 + 2 = 0.677124344 x2 = 0.677124344 Simplifying x2 = 0.677124344 Take the square root of each side: x = {-0.822875655, 0.822875655}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.822875656, 1.822875656, -0.822875655, 0.822875655}

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