2x^2+4xy+3y^2-2xz-2yz+z^2+1=t+sqrt(y+z-t)

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Solution for 2x^2+4xy+3y^2-2xz-2yz+z^2+1=t+sqrt(y+z-t) equation: 


Simplifying
2x2 + 4xy + 3y2 + -2xz + -2yz + z2 + 1 = t + sqrt(y + z + -1t)

Reorder the terms:
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = t + sqrt(y + z + -1t)

Reorder the terms:
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = t + qrst(-1t + y + z)
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = t + (-1t * qrst + y * qrst + z * qrst)

Reorder the terms:
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = t + (qrsty + qrstz + -1qrst2)
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = t + (qrsty + qrstz + -1qrst2)

Reorder the terms:
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = qrsty + qrstz + -1qrst2 + t

Solving
1 + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = qrsty + qrstz + -1qrst2 + t

Solving for variable 'x'.

Reorder the terms:
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = qrsty + qrstz + -1qrst2 + t + -1qrsty + -1qrstz + qrst2 + -1t

Reorder the terms:
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = qrsty + -1qrsty + qrstz + -1qrstz + -1qrst2 + qrst2 + t + -1t

Combine like terms: qrsty + -1qrsty = 0
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = 0 + qrstz + -1qrstz + -1qrst2 + qrst2 + t + -1t
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = qrstz + -1qrstz + -1qrst2 + qrst2 + t + -1t

Combine like terms: qrstz + -1qrstz = 0
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = 0 + -1qrst2 + qrst2 + t + -1t
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = -1qrst2 + qrst2 + t + -1t

Combine like terms: -1qrst2 + qrst2 = 0
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = 0 + t + -1t
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = t + -1t

Combine like terms: t + -1t = 0
1 + -1qrsty + -1qrstz + qrst2 + -1t + 4xy + -2xz + 2x2 + -2yz + 3y2 + z2 = 0

The solution to this equation could not be determined.

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