x^4-41x^2=400

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Solution for x^4-41x^2=400 equation:


Simplifying
x4 + -41x2 = 400

Reorder the terms:
-41x2 + x4 = 400

Solving
-41x2 + x4 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + -41x2 + x4 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + -41x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -41x2 + 400 + x4 = 0 + 400

Reorder the terms:
-400 + 400 + -41x2 + x4 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -41x2 + x4 = 0 + 400
-41x2 + x4 = 0 + 400

Combine like terms: 0 + 400 = 400
-41x2 + x4 = 400

The x term is -41x2.  Take half its coefficient (-20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
-41x2 + 420.25 + x4 = 400 + 420.25

Reorder the terms:
420.25 + -41x2 + x4 = 400 + 420.25

Combine like terms: 400 + 420.25 = 820.25
420.25 + -41x2 + x4 = 820.25

Factor a perfect square on the left side:
(x2 + -20.5)(x2 + -20.5) = 820.25

Calculate the square root of the right side: 28.640006983

Break this problem into two subproblems by setting 
(x2 + -20.5) equal to 28.640006983 and -28.640006983.

Subproblem 1

x2 + -20.5 = 28.640006983 Simplifying x2 + -20.5 = 28.640006983 Reorder the terms: -20.5 + x2 = 28.640006983 Solving -20.5 + x2 = 28.640006983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x2 = 28.640006983 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x2 = 28.640006983 + 20.5 x2 = 28.640006983 + 20.5 Combine like terms: 28.640006983 + 20.5 = 49.140006983 x2 = 49.140006983 Simplifying x2 = 49.140006983 Take the square root of each side: x = {-7.009993365, 7.009993365}

Subproblem 2

x2 + -20.5 = -28.640006983 Simplifying x2 + -20.5 = -28.640006983 Reorder the terms: -20.5 + x2 = -28.640006983 Solving -20.5 + x2 = -28.640006983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x2 = -28.640006983 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x2 = -28.640006983 + 20.5 x2 = -28.640006983 + 20.5 Combine like terms: -28.640006983 + 20.5 = -8.140006983 x2 = -8.140006983 Simplifying x2 = -8.140006983 Reorder the terms: 8.140006983 + x2 = -8.140006983 + 8.140006983 Combine like terms: -8.140006983 + 8.140006983 = 0.000000000 8.140006983 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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