2x^2+2y^2+z^2+8yz-z+8=0

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Solution for 2x^2+2y^2+z^2+8yz-z+8=0 equation: 


Simplifying
2x2 + 2y2 + z2 + 8yz + -1z + 8 = 0

Reorder the terms:
8 + 2x2 + 8yz + 2y2 + -1z + z2 = 0

Solving
8 + 2x2 + 8yz + 2y2 + -1z + z2 = 0

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + 2x2 + 8yz + 2y2 + -1z + -8 + z2 = 0 + -8

Reorder the terms:
8 + -8 + 2x2 + 8yz + 2y2 + -1z + z2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 2x2 + 8yz + 2y2 + -1z + z2 = 0 + -8
2x2 + 8yz + 2y2 + -1z + z2 = 0 + -8

Combine like terms: 0 + -8 = -8
2x2 + 8yz + 2y2 + -1z + z2 = -8

Add '-8yz' to each side of the equation.
2x2 + 8yz + 2y2 + -1z + -8yz + z2 = -8 + -8yz

Reorder the terms:
2x2 + 8yz + -8yz + 2y2 + -1z + z2 = -8 + -8yz

Combine like terms: 8yz + -8yz = 0
2x2 + 0 + 2y2 + -1z + z2 = -8 + -8yz
2x2 + 2y2 + -1z + z2 = -8 + -8yz

Add '-2y2' to each side of the equation.
2x2 + 2y2 + -1z + -2y2 + z2 = -8 + -8yz + -2y2

Reorder the terms:
2x2 + 2y2 + -2y2 + -1z + z2 = -8 + -8yz + -2y2

Combine like terms: 2y2 + -2y2 = 0
2x2 + 0 + -1z + z2 = -8 + -8yz + -2y2
2x2 + -1z + z2 = -8 + -8yz + -2y2

Add 'z' to each side of the equation.
2x2 + -1z + z + z2 = -8 + -8yz + -2y2 + z

Combine like terms: -1z + z = 0
2x2 + 0 + z2 = -8 + -8yz + -2y2 + z
2x2 + z2 = -8 + -8yz + -2y2 + z

Add '-1z2' to each side of the equation.
2x2 + z2 + -1z2 = -8 + -8yz + -2y2 + z + -1z2

Combine like terms: z2 + -1z2 = 0
2x2 + 0 = -8 + -8yz + -2y2 + z + -1z2
2x2 = -8 + -8yz + -2y2 + z + -1z2

Divide each side by '2'.
x2 = -4 + -4yz + -1y2 + 0.5z + -0.5z2

Simplifying
x2 = -4 + -4yz + -1y2 + 0.5z + -0.5z2

Reorder the terms:
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = -4 + -4yz + -1y2 + 0.5z + -0.5z2 + 4 + 4yz + y2 + -0.5z + 0.5z2

Reorder the terms:
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = -4 + 4 + -4yz + 4yz + -1y2 + y2 + 0.5z + -0.5z + -0.5z2 + 0.5z2

Combine like terms: -4 + 4 = 0
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = 0 + -4yz + 4yz + -1y2 + y2 + 0.5z + -0.5z + -0.5z2 + 0.5z2
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = -4yz + 4yz + -1y2 + y2 + 0.5z + -0.5z + -0.5z2 + 0.5z2

Combine like terms: -4yz + 4yz = 0
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = 0 + -1y2 + y2 + 0.5z + -0.5z + -0.5z2 + 0.5z2
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = -1y2 + y2 + 0.5z + -0.5z + -0.5z2 + 0.5z2

Combine like terms: -1y2 + y2 = 0
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = 0 + 0.5z + -0.5z + -0.5z2 + 0.5z2
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = 0.5z + -0.5z + -0.5z2 + 0.5z2

Combine like terms: 0.5z + -0.5z = 0.0
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = 0.0 + -0.5z2 + 0.5z2
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = -0.5z2 + 0.5z2

Combine like terms: -0.5z2 + 0.5z2 = 0.0
4 + x2 + 4yz + y2 + -0.5z + 0.5z2 = 0.0

The solution to this equation could not be determined.

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