x^4+71x^2-2700=0

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Solution for x^4+71x^2-2700=0 equation:


Simplifying
x4 + 71x2 + -2700 = 0

Reorder the terms:
-2700 + 71x2 + x4 = 0

Solving
-2700 + 71x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2700' to each side of the equation.
-2700 + 71x2 + 2700 + x4 = 0 + 2700

Reorder the terms:
-2700 + 2700 + 71x2 + x4 = 0 + 2700

Combine like terms: -2700 + 2700 = 0
0 + 71x2 + x4 = 0 + 2700
71x2 + x4 = 0 + 2700

Combine like terms: 0 + 2700 = 2700
71x2 + x4 = 2700

The x term is 71x2.  Take half its coefficient (35.5).
Square it (1260.25) and add it to both sides.

Add '1260.25' to each side of the equation.
71x2 + 1260.25 + x4 = 2700 + 1260.25

Reorder the terms:
1260.25 + 71x2 + x4 = 2700 + 1260.25

Combine like terms: 2700 + 1260.25 = 3960.25
1260.25 + 71x2 + x4 = 3960.25

Factor a perfect square on the left side:
(x2 + 35.5)(x2 + 35.5) = 3960.25

Calculate the square root of the right side: 62.930517239

Break this problem into two subproblems by setting 
(x2 + 35.5) equal to 62.930517239 and -62.930517239.

Subproblem 1

x2 + 35.5 = 62.930517239 Simplifying x2 + 35.5 = 62.930517239 Reorder the terms: 35.5 + x2 = 62.930517239 Solving 35.5 + x2 = 62.930517239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x2 = 62.930517239 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x2 = 62.930517239 + -35.5 x2 = 62.930517239 + -35.5 Combine like terms: 62.930517239 + -35.5 = 27.430517239 x2 = 27.430517239 Simplifying x2 = 27.430517239 Take the square root of each side: x = {-5.23741513, 5.23741513}

Subproblem 2

x2 + 35.5 = -62.930517239 Simplifying x2 + 35.5 = -62.930517239 Reorder the terms: 35.5 + x2 = -62.930517239 Solving 35.5 + x2 = -62.930517239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x2 = -62.930517239 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x2 = -62.930517239 + -35.5 x2 = -62.930517239 + -35.5 Combine like terms: -62.930517239 + -35.5 = -98.430517239 x2 = -98.430517239 Simplifying x2 = -98.430517239 Reorder the terms: 98.430517239 + x2 = -98.430517239 + 98.430517239 Combine like terms: -98.430517239 + 98.430517239 = 0.000000000 98.430517239 + 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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