x*x*x*x+x*x=7

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Solution for x*x*x*x+x*x=7 equation: 


Simplifying
x * x * x * x + x * x = 7

Multiply x * x
x2 * x * x + x * x = 7

Multiply x2 * x
x3 * x + x * x = 7

Multiply x3 * x
x4 + x * x = 7

Multiply x * x
x4 + x2 = 7

Reorder the terms:
x2 + x4 = 7

Solving
x2 + x4 = 7

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x2 + 0.25 + x4 = 7 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + x2 + x4 = 7.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
x2 + 0.5 = 2.692582404

Simplifying
x2 + 0.5 = 2.692582404

Reorder the terms:
0.5 + x2 = 2.692582404

Solving
0.5 + x2 = 2.692582404

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 2.692582404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 2.692582404 + -0.5
x2 = 2.692582404 + -0.5

Combine like terms: 2.692582404 + -0.5 = 2.192582404
x2 = 2.192582404

Simplifying
x2 = 2.192582404

Take the square root of each side:
x = {-1.480737115, 1.480737115}


Subproblem 2
x2 + 0.5 = -2.692582404

Simplifying
x2 + 0.5 = -2.692582404

Reorder the terms:
0.5 + x2 = -2.692582404

Solving
0.5 + x2 = -2.692582404

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = -2.692582404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -2.692582404 + -0.5
x2 = -2.692582404 + -0.5

Combine like terms: -2.692582404 + -0.5 = -3.192582404
x2 = -3.192582404

Simplifying
x2 = -3.192582404

Reorder the terms:
3.192582404 + x2 = -3.192582404 + 3.192582404

Combine like terms: -3.192582404 + 3.192582404 = 0.000000000
3.192582404 + 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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