x^2+y^2+w^2+z^2=48117

Solution for x^2+y^2+w^2+z^2=48117 equation:

Simplifying
x2 + y2 + w2 + z2 = 48117

Reorder the terms:
w2 + x2 + y2 + z2 = 48117

Solving
w2 + x2 + y2 + z2 = 48117

Solving for variable 'w'.

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

Add '-1x2' to each side of the equation.
w2 + x2 + y2 + -1x2 + z2 = 48117 + -1x2

Reorder the terms:
w2 + x2 + -1x2 + y2 + z2 = 48117 + -1x2

Combine like terms: x2 + -1x2 = 0
w2 + 0 + y2 + z2 = 48117 + -1x2
w2 + y2 + z2 = 48117 + -1x2

Add '-1y2' to each side of the equation.
w2 + y2 + -1y2 + z2 = 48117 + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
w2 + 0 + z2 = 48117 + -1x2 + -1y2
w2 + z2 = 48117 + -1x2 + -1y2

Add '-1z2' to each side of the equation.
w2 + z2 + -1z2 = 48117 + -1x2 + -1y2 + -1z2

Combine like terms: z2 + -1z2 = 0
w2 + 0 = 48117 + -1x2 + -1y2 + -1z2
w2 = 48117 + -1x2 + -1y2 + -1z2

Simplifying
w2 = 48117 + -1x2 + -1y2 + -1z2

Reorder the terms:
-48117 + w2 + x2 + y2 + z2 = 48117 + -1x2 + -1y2 + -1z2 + -48117 + x2 + y2 + z2

Reorder the terms:
-48117 + w2 + x2 + y2 + z2 = 48117 + -48117 + -1x2 + x2 + -1y2 + y2 + -1z2 + z2

Combine like terms: 48117 + -48117 = 0
-48117 + w2 + x2 + y2 + z2 = 0 + -1x2 + x2 + -1y2 + y2 + -1z2 + z2
-48117 + w2 + x2 + y2 + z2 = -1x2 + x2 + -1y2 + y2 + -1z2 + z2

Combine like terms: -1x2 + x2 = 0
-48117 + w2 + x2 + y2 + z2 = 0 + -1y2 + y2 + -1z2 + z2
-48117 + w2 + x2 + y2 + z2 = -1y2 + y2 + -1z2 + z2

Combine like terms: -1y2 + y2 = 0
-48117 + w2 + x2 + y2 + z2 = 0 + -1z2 + z2
-48117 + w2 + x2 + y2 + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-48117 + w2 + x2 + y2 + z2 = 0

The solution to this equation could not be determined.