x^4-172x^2+576=0

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Solution for x^4-172x^2+576=0 equation:


Simplifying
x4 + -172x2 + 576 = 0

Reorder the terms:
576 + -172x2 + x4 = 0

Solving
576 + -172x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-576' to each side of the equation.
576 + -172x2 + -576 + x4 = 0 + -576

Reorder the terms:
576 + -576 + -172x2 + x4 = 0 + -576

Combine like terms: 576 + -576 = 0
0 + -172x2 + x4 = 0 + -576
-172x2 + x4 = 0 + -576

Combine like terms: 0 + -576 = -576
-172x2 + x4 = -576

The x term is -172x2.  Take half its coefficient (-86).
Square it (7396) and add it to both sides.

Add '7396' to each side of the equation.
-172x2 + 7396 + x4 = -576 + 7396

Reorder the terms:
7396 + -172x2 + x4 = -576 + 7396

Combine like terms: -576 + 7396 = 6820
7396 + -172x2 + x4 = 6820

Factor a perfect square on the left side:
(x2 + -86)(x2 + -86) = 6820

Calculate the square root of the right side: 82.583291288

Break this problem into two subproblems by setting 
(x2 + -86) equal to 82.583291288 and -82.583291288.

Subproblem 1

x2 + -86 = 82.583291288 Simplifying x2 + -86 = 82.583291288 Reorder the terms: -86 + x2 = 82.583291288 Solving -86 + x2 = 82.583291288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '86' to each side of the equation. -86 + 86 + x2 = 82.583291288 + 86 Combine like terms: -86 + 86 = 0 0 + x2 = 82.583291288 + 86 x2 = 82.583291288 + 86 Combine like terms: 82.583291288 + 86 = 168.583291288 x2 = 168.583291288 Simplifying x2 = 168.583291288 Take the square root of each side: x = {-12.98396285, 12.98396285}

Subproblem 2

x2 + -86 = -82.583291288 Simplifying x2 + -86 = -82.583291288 Reorder the terms: -86 + x2 = -82.583291288 Solving -86 + x2 = -82.583291288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '86' to each side of the equation. -86 + 86 + x2 = -82.583291288 + 86 Combine like terms: -86 + 86 = 0 0 + x2 = -82.583291288 + 86 x2 = -82.583291288 + 86 Combine like terms: -82.583291288 + 86 = 3.416708712 x2 = 3.416708712 Simplifying x2 = 3.416708712 Take the square root of each side: x = {-1.848434124, 1.848434124}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-12.98396285, 12.98396285, -1.848434124, 1.848434124}

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