7(x^2+y^2)+90*sqrt(2)*(x+y)-50*x*y-162=0

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Solution for 7(x^2+y^2)+90*sqrt(2)*(x+y)-50*x*y-162=0 equation: 


Simplifying
7(x2 + y2) + 90sqrt(2)(x + y) + -50x * y + -162 = 0
(x2 * 7 + y2 * 7) + 90sqrt(2)(x + y) + -50x * y + -162 = 0
(7x2 + 7y2) + 90sqrt(2)(x + y) + -50x * y + -162 = 0

Reorder the terms for easier multiplication:
7x2 + 7y2 + 90 * 2qrst(x + y) + -50x * y + -162 = 0

Multiply 90 * 2
7x2 + 7y2 + 180qrst(x + y) + -50x * y + -162 = 0
7x2 + 7y2 + (x * 180qrst + y * 180qrst) + -50x * y + -162 = 0
7x2 + 7y2 + (180qrstx + 180qrsty) + -50x * y + -162 = 0

Multiply x * y
7x2 + 7y2 + 180qrstx + 180qrsty + -50xy + -162 = 0

Reorder the terms:
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0

Solving
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0

Solving for variable 'q'.

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

Add '162' to each side of the equation.
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 162 + 7y2 = 0 + 162

Reorder the terms:
-162 + 162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0 + 162
180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0 + 162

Combine like terms: 0 + 162 = 162
180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 162

Add '50xy' to each side of the equation.
180qrstx + 180qrsty + -50xy + 7x2 + 50xy + 7y2 = 162 + 50xy

Reorder the terms:
180qrstx + 180qrsty + -50xy + 50xy + 7x2 + 7y2 = 162 + 50xy

Combine like terms: -50xy + 50xy = 0
180qrstx + 180qrsty + 0 + 7x2 + 7y2 = 162 + 50xy
180qrstx + 180qrsty + 7x2 + 7y2 = 162 + 50xy

Add '-7x2' to each side of the equation.
180qrstx + 180qrsty + 7x2 + -7x2 + 7y2 = 162 + 50xy + -7x2

Combine like terms: 7x2 + -7x2 = 0
180qrstx + 180qrsty + 0 + 7y2 = 162 + 50xy + -7x2
180qrstx + 180qrsty + 7y2 = 162 + 50xy + -7x2

Add '-7y2' to each side of the equation.
180qrstx + 180qrsty + 7y2 + -7y2 = 162 + 50xy + -7x2 + -7y2

Combine like terms: 7y2 + -7y2 = 0
180qrstx + 180qrsty + 0 = 162 + 50xy + -7x2 + -7y2
180qrstx + 180qrsty = 162 + 50xy + -7x2 + -7y2

Reorder the terms:
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 162 + 50xy + -7x2 + -7y2 + -162 + -50xy + 7x2 + 7y2

Reorder the terms:
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 162 + -162 + 50xy + -50xy + -7x2 + 7x2 + -7y2 + 7y2

Combine like terms: 162 + -162 = 0
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0 + 50xy + -50xy + -7x2 + 7x2 + -7y2 + 7y2
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 50xy + -50xy + -7x2 + 7x2 + -7y2 + 7y2

Combine like terms: 50xy + -50xy = 0
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0 + -7x2 + 7x2 + -7y2 + 7y2
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = -7x2 + 7x2 + -7y2 + 7y2

Combine like terms: -7x2 + 7x2 = 0
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0 + -7y2 + 7y2
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = -7y2 + 7y2

Combine like terms: -7y2 + 7y2 = 0
-162 + 180qrstx + 180qrsty + -50xy + 7x2 + 7y2 = 0

The solution to this equation could not be determined.

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