2x^2+4y^2-z^2-2z=100

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Solution for 2x^2+4y^2-z^2-2z=100 equation: 


Simplifying
2x2 + 4y2 + -1z2 + -2z = 100

Reorder the terms:
2x2 + 4y2 + -2z + -1z2 = 100

Solving
2x2 + 4y2 + -2z + -1z2 = 100

Solving for variable 'x'.

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

Add '-4y2' to each side of the equation.
2x2 + 4y2 + -2z + -4y2 + -1z2 = 100 + -4y2

Reorder the terms:
2x2 + 4y2 + -4y2 + -2z + -1z2 = 100 + -4y2

Combine like terms: 4y2 + -4y2 = 0
2x2 + 0 + -2z + -1z2 = 100 + -4y2
2x2 + -2z + -1z2 = 100 + -4y2

Add '2z' to each side of the equation.
2x2 + -2z + 2z + -1z2 = 100 + -4y2 + 2z

Combine like terms: -2z + 2z = 0
2x2 + 0 + -1z2 = 100 + -4y2 + 2z
2x2 + -1z2 = 100 + -4y2 + 2z

Add 'z2' to each side of the equation.
2x2 + -1z2 + z2 = 100 + -4y2 + 2z + z2

Combine like terms: -1z2 + z2 = 0
2x2 + 0 = 100 + -4y2 + 2z + z2
2x2 = 100 + -4y2 + 2z + z2

Divide each side by '2'.
x2 = 50 + -2y2 + z + 0.5z2

Simplifying
x2 = 50 + -2y2 + z + 0.5z2

Reorder the terms:
-50 + x2 + 2y2 + -1z + -0.5z2 = 50 + -2y2 + z + 0.5z2 + -50 + 2y2 + -1z + -0.5z2

Reorder the terms:
-50 + x2 + 2y2 + -1z + -0.5z2 = 50 + -50 + -2y2 + 2y2 + z + -1z + 0.5z2 + -0.5z2

Combine like terms: 50 + -50 = 0
-50 + x2 + 2y2 + -1z + -0.5z2 = 0 + -2y2 + 2y2 + z + -1z + 0.5z2 + -0.5z2
-50 + x2 + 2y2 + -1z + -0.5z2 = -2y2 + 2y2 + z + -1z + 0.5z2 + -0.5z2

Combine like terms: -2y2 + 2y2 = 0
-50 + x2 + 2y2 + -1z + -0.5z2 = 0 + z + -1z + 0.5z2 + -0.5z2
-50 + x2 + 2y2 + -1z + -0.5z2 = z + -1z + 0.5z2 + -0.5z2

Combine like terms: z + -1z = 0
-50 + x2 + 2y2 + -1z + -0.5z2 = 0 + 0.5z2 + -0.5z2
-50 + x2 + 2y2 + -1z + -0.5z2 = 0.5z2 + -0.5z2

Combine like terms: 0.5z2 + -0.5z2 = 0.0
-50 + x2 + 2y2 + -1z + -0.5z2 = 0.0

The solution to this equation could not be determined.

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