x^4-20x^2+16=0

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Solution for x^4-20x^2+16=0 equation:


Simplifying
x4 + -20x2 + 16 = 0

Reorder the terms:
16 + -20x2 + x4 = 0

Solving
16 + -20x2 + 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 + -20x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + -20x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -20x2 + x4 = 0 + -16
-20x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
-20x2 + x4 = -16

The x term is -20x2.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x2 + 100 + x4 = -16 + 100

Reorder the terms:
100 + -20x2 + x4 = -16 + 100

Combine like terms: -16 + 100 = 84
100 + -20x2 + x4 = 84

Factor a perfect square on the left side:
(x2 + -10)(x2 + -10) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x2 + -10) equal to 9.16515139 and -9.16515139.

Subproblem 1

x2 + -10 = 9.16515139 Simplifying x2 + -10 = 9.16515139 Reorder the terms: -10 + x2 = 9.16515139 Solving -10 + x2 = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 9.16515139 + 10 x2 = 9.16515139 + 10 Combine like terms: 9.16515139 + 10 = 19.16515139 x2 = 19.16515139 Simplifying x2 = 19.16515139 Take the square root of each side: x = {-4.377802119, 4.377802119}

Subproblem 2

x2 + -10 = -9.16515139 Simplifying x2 + -10 = -9.16515139 Reorder the terms: -10 + x2 = -9.16515139 Solving -10 + x2 = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -9.16515139 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -9.16515139 + 10 x2 = -9.16515139 + 10 Combine like terms: -9.16515139 + 10 = 0.83484861 x2 = 0.83484861 Simplifying x2 = 0.83484861 Take the square root of each side: x = {-0.913700503, 0.913700503}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.377802119, 4.377802119, -0.913700503, 0.913700503}

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