x^4-1+15=14x^2-14

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Solution for x^4-1+15=14x^2-14 equation:


Simplifying
x4 + -1 + 15 = 14x2 + -14

Reorder the terms:
-1 + 15 + x4 = 14x2 + -14

Combine like terms: -1 + 15 = 14
14 + x4 = 14x2 + -14

Reorder the terms:
14 + x4 = -14 + 14x2

Solving
14 + x4 = -14 + 14x2

Solving for variable 'x'.

Reorder the terms:
14 + 14 + -14x2 + x4 = -14 + 14x2 + 14 + -14x2

Combine like terms: 14 + 14 = 28
28 + -14x2 + x4 = -14 + 14x2 + 14 + -14x2

Reorder the terms:
28 + -14x2 + x4 = -14 + 14 + 14x2 + -14x2

Combine like terms: -14 + 14 = 0
28 + -14x2 + x4 = 0 + 14x2 + -14x2
28 + -14x2 + x4 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
28 + -14x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -14x2 + -28 + x4 = 0 + -28

Reorder the terms:
28 + -28 + -14x2 + x4 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -14x2 + x4 = 0 + -28
-14x2 + x4 = 0 + -28

Combine like terms: 0 + -28 = -28
-14x2 + x4 = -28

The x term is -14x2.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x2 + 49 + x4 = -28 + 49

Reorder the terms:
49 + -14x2 + x4 = -28 + 49

Combine like terms: -28 + 49 = 21
49 + -14x2 + x4 = 21

Factor a perfect square on the left side:
(x2 + -7)(x2 + -7) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x2 + -7) equal to 4.582575695 and -4.582575695.

Subproblem 1

x2 + -7 = 4.582575695 Simplifying x2 + -7 = 4.582575695 Reorder the terms: -7 + x2 = 4.582575695 Solving -7 + x2 = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 4.582575695 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 4.582575695 + 7 x2 = 4.582575695 + 7 Combine like terms: 4.582575695 + 7 = 11.582575695 x2 = 11.582575695 Simplifying x2 = 11.582575695 Take the square root of each side: x = {-3.403318336, 3.403318336}

Subproblem 2

x2 + -7 = -4.582575695 Simplifying x2 + -7 = -4.582575695 Reorder the terms: -7 + x2 = -4.582575695 Solving -7 + x2 = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -4.582575695 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -4.582575695 + 7 x2 = -4.582575695 + 7 Combine like terms: -4.582575695 + 7 = 2.417424305 x2 = 2.417424305 Simplifying x2 = 2.417424305 Take the square root of each side: x = {-1.554806838, 1.554806838}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.403318336, 3.403318336, -1.554806838, 1.554806838}

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