y-x^2+8=y+8-x

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


Simplifying
y + -1x2 + 8 = y + 8 + -1x

Reorder the terms:
8 + -1x2 + y = y + 8 + -1x

Reorder the terms:
8 + -1x2 + y = 8 + -1x + y

Add '-8' to each side of the equation.
8 + -1x2 + -8 + y = 8 + -1x + -8 + y

Reorder the terms:
8 + -8 + -1x2 + y = 8 + -1x + -8 + y

Combine like terms: 8 + -8 = 0
0 + -1x2 + y = 8 + -1x + -8 + y
-1x2 + y = 8 + -1x + -8 + y

Reorder the terms:
-1x2 + y = 8 + -8 + -1x + y

Combine like terms: 8 + -8 = 0
-1x2 + y = 0 + -1x + y
-1x2 + y = -1x + y

Add '-1y' to each side of the equation.
-1x2 + y + -1y = -1x + y + -1y

Combine like terms: y + -1y = 0
-1x2 + 0 = -1x + y + -1y
-1x2 = -1x + y + -1y

Combine like terms: y + -1y = 0
-1x2 = -1x + 0
-1x2 = -1x

Solving
-1x2 = -1x

Solving for variable 'x'.

Reorder the terms:
x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {0, 1}

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