(n^4-10)(n^4+8)=39

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Solution for (n^4-10)(n^4+8)=39 equation:


Simplifying
(n4 + -10)(n4 + 8) = 39

Reorder the terms:
(-10 + n4)(n4 + 8) = 39

Reorder the terms:
(-10 + n4)(8 + n4) = 39

Multiply (-10 + n4) * (8 + n4)
(-10(8 + n4) + n4(8 + n4)) = 39
((8 * -10 + n4 * -10) + n4(8 + n4)) = 39
((-80 + -10n4) + n4(8 + n4)) = 39
(-80 + -10n4 + (8 * n4 + n4 * n4)) = 39
(-80 + -10n4 + (8n4 + n8)) = 39

Combine like terms: -10n4 + 8n4 = -2n4
(-80 + -2n4 + n8) = 39

Solving
-80 + -2n4 + n8 = 39

Solving for variable 'n'.

Reorder the terms:
-80 + -39 + -2n4 + n8 = 39 + -39

Combine like terms: -80 + -39 = -119
-119 + -2n4 + n8 = 39 + -39

Combine like terms: 39 + -39 = 0
-119 + -2n4 + n8 = 0

Begin completing the square.

Move the constant term to the right:

Add '119' to each side of the equation.
-119 + -2n4 + 119 + n8 = 0 + 119

Reorder the terms:
-119 + 119 + -2n4 + n8 = 0 + 119

Combine like terms: -119 + 119 = 0
0 + -2n4 + n8 = 0 + 119
-2n4 + n8 = 0 + 119

Combine like terms: 0 + 119 = 119
-2n4 + n8 = 119

The n term is -2n4.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n4 + 1 + n8 = 119 + 1

Reorder the terms:
1 + -2n4 + n8 = 119 + 1

Combine like terms: 119 + 1 = 120
1 + -2n4 + n8 = 120

Factor a perfect square on the left side:
(n4 + -1)(n4 + -1) = 120

Calculate the square root of the right side: 10.95445115

Break this problem into two subproblems by setting 
(n4 + -1) equal to 10.95445115 and -10.95445115.

Subproblem 1

n4 + -1 = 10.95445115 Simplifying n4 + -1 = 10.95445115 Reorder the terms: -1 + n4 = 10.95445115 Solving -1 + n4 = 10.95445115 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n4 = 10.95445115 + 1 Combine like terms: -1 + 1 = 0 0 + n4 = 10.95445115 + 1 n4 = 10.95445115 + 1 Combine like terms: 10.95445115 + 1 = 11.95445115 n4 = 11.95445115 Simplifying n4 = 11.95445115 Reorder the terms: -11.95445115 + n4 = 11.95445115 + -11.95445115 Combine like terms: 11.95445115 + -11.95445115 = 0.00000000 -11.95445115 + n4 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

n4 + -1 = -10.95445115 Simplifying n4 + -1 = -10.95445115 Reorder the terms: -1 + n4 = -10.95445115 Solving -1 + n4 = -10.95445115 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n4 = -10.95445115 + 1 Combine like terms: -1 + 1 = 0 0 + n4 = -10.95445115 + 1 n4 = -10.95445115 + 1 Combine like terms: -10.95445115 + 1 = -9.95445115 n4 = -9.95445115 Simplifying n4 = -9.95445115 Reorder the terms: 9.95445115 + n4 = -9.95445115 + 9.95445115 Combine like terms: -9.95445115 + 9.95445115 = 0.00000000 9.95445115 + n4 = 0.00000000 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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