x^4-18x^2+16=0

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Solution for x^4-18x^2+16=0 equation:


Simplifying
x4 + -18x2 + 16 = 0

Reorder the terms:
16 + -18x2 + x4 = 0

Solving
16 + -18x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -18x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + -18x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -18x2 + x4 = 0 + -16
-18x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
-18x2 + x4 = -16

The x term is -18x2.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x2 + 81 + x4 = -16 + 81

Reorder the terms:
81 + -18x2 + x4 = -16 + 81

Combine like terms: -16 + 81 = 65
81 + -18x2 + x4 = 65

Factor a perfect square on the left side:
(x2 + -9)(x2 + -9) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x2 + -9) equal to 8.062257748 and -8.062257748.

Subproblem 1

x2 + -9 = 8.062257748 Simplifying x2 + -9 = 8.062257748 Reorder the terms: -9 + x2 = 8.062257748 Solving -9 + x2 = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 8.062257748 + 9 x2 = 8.062257748 + 9 Combine like terms: 8.062257748 + 9 = 17.062257748 x2 = 17.062257748 Simplifying x2 = 17.062257748 Take the square root of each side: x = {-4.130648587, 4.130648587}

Subproblem 2

x2 + -9 = -8.062257748 Simplifying x2 + -9 = -8.062257748 Reorder the terms: -9 + x2 = -8.062257748 Solving -9 + x2 = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = -8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -8.062257748 + 9 x2 = -8.062257748 + 9 Combine like terms: -8.062257748 + 9 = 0.937742252 x2 = 0.937742252 Simplifying x2 = 0.937742252 Take the square root of each side: x = {-0.968370927, 0.968370927}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.130648587, 4.130648587, -0.968370927, 0.968370927}

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