x^4=8x^2+7

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Solution for x^4=8x^2+7 equation: 


Simplifying
x4 = 8x2 + 7

Reorder the terms:
x4 = 7 + 8x2

Solving
x4 = 7 + 8x2

Solving for variable 'x'.

Reorder the terms:
-7 + -8x2 + x4 = 7 + 8x2 + -7 + -8x2

Reorder the terms:
-7 + -8x2 + x4 = 7 + -7 + 8x2 + -8x2

Combine like terms: 7 + -7 = 0
-7 + -8x2 + x4 = 0 + 8x2 + -8x2
-7 + -8x2 + x4 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-7 + -8x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8x2 + 7 + x4 = 0 + 7

Reorder the terms:
-7 + 7 + -8x2 + x4 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8x2 + x4 = 0 + 7
-8x2 + x4 = 0 + 7

Combine like terms: 0 + 7 = 7
-8x2 + x4 = 7

The x term is -8x2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x2 + 16 + x4 = 7 + 16

Reorder the terms:
16 + -8x2 + x4 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + -8x2 + x4 = 23

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x2 + -4) equal to 4.795831523 and -4.795831523.


Subproblem 1
x2 + -4 = 4.795831523

Simplifying
x2 + -4 = 4.795831523

Reorder the terms:
-4 + x2 = 4.795831523

Solving
-4 + x2 = 4.795831523

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = 4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = 4.795831523 + 4
x2 = 4.795831523 + 4

Combine like terms: 4.795831523 + 4 = 8.795831523
x2 = 8.795831523

Simplifying
x2 = 8.795831523

Take the square root of each side:
x = {-2.965776715, 2.965776715}


Subproblem 2
x2 + -4 = -4.795831523

Simplifying
x2 + -4 = -4.795831523

Reorder the terms:
-4 + x2 = -4.795831523

Solving
-4 + x2 = -4.795831523

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = -4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = -4.795831523 + 4
x2 = -4.795831523 + 4

Combine like terms: -4.795831523 + 4 = -0.795831523
x2 = -0.795831523

Simplifying
x2 = -0.795831523

Reorder the terms:
0.795831523 + x2 = -0.795831523 + 0.795831523

Combine like terms: -0.795831523 + 0.795831523 = 0.000000000
0.795831523 + 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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