h^4-1255h^2-345744=0

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Solution for h^4-1255h^2-345744=0 equation: 


Simplifying
h4 + -1255h2 + -345744 = 0

Reorder the terms:
-345744 + -1255h2 + h4 = 0

Solving
-345744 + -1255h2 + h4 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '345744' to each side of the equation.
-345744 + -1255h2 + 345744 + h4 = 0 + 345744

Reorder the terms:
-345744 + 345744 + -1255h2 + h4 = 0 + 345744

Combine like terms: -345744 + 345744 = 0
0 + -1255h2 + h4 = 0 + 345744
-1255h2 + h4 = 0 + 345744

Combine like terms: 0 + 345744 = 345744
-1255h2 + h4 = 345744

The h term is -1255h2.  Take half its coefficient (-627.5).
Square it (393756.25) and add it to both sides.

Add '393756.25' to each side of the equation.
-1255h2 + 393756.25 + h4 = 345744 + 393756.25

Reorder the terms:
393756.25 + -1255h2 + h4 = 345744 + 393756.25

Combine like terms: 345744 + 393756.25 = 739500.25
393756.25 + -1255h2 + h4 = 739500.25

Factor a perfect square on the left side:
(h2 + -627.5)(h2 + -627.5) = 739500.25

Calculate the square root of the right side: 859.942003858

Break this problem into two subproblems by setting 
(h2 + -627.5) equal to 859.942003858 and -859.942003858.


Subproblem 1
h2 + -627.5 = 859.942003858

Simplifying
h2 + -627.5 = 859.942003858

Reorder the terms:
-627.5 + h2 = 859.942003858

Solving
-627.5 + h2 = 859.942003858

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '627.5' to each side of the equation.
-627.5 + 627.5 + h2 = 859.942003858 + 627.5

Combine like terms: -627.5 + 627.5 = 0.0
0.0 + h2 = 859.942003858 + 627.5
h2 = 859.942003858 + 627.5

Combine like terms: 859.942003858 + 627.5 = 1487.442003858
h2 = 1487.442003858

Simplifying
h2 = 1487.442003858

Take the square root of each side:
h = {-38.567369678, 38.567369678}


Subproblem 2
h2 + -627.5 = -859.942003858

Simplifying
h2 + -627.5 = -859.942003858

Reorder the terms:
-627.5 + h2 = -859.942003858

Solving
-627.5 + h2 = -859.942003858

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '627.5' to each side of the equation.
-627.5 + 627.5 + h2 = -859.942003858 + 627.5

Combine like terms: -627.5 + 627.5 = 0.0
0.0 + h2 = -859.942003858 + 627.5
h2 = -859.942003858 + 627.5

Combine like terms: -859.942003858 + 627.5 = -232.442003858
h2 = -232.442003858

Simplifying
h2 = -232.442003858

Reorder the terms:
232.442003858 + h2 = -232.442003858 + 232.442003858

Combine like terms: -232.442003858 + 232.442003858 = 0.000000000
232.442003858 + h2 = 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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