1-2x=1+x^2

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Solution for 1-2x=1+x^2 equation: 


Simplifying
1 + -2x = 1 + x2

Add '-1' to each side of the equation.
1 + -1 + -2x = 1 + -1 + x2

Combine like terms: 1 + -1 = 0
0 + -2x = 1 + -1 + x2
-2x = 1 + -1 + x2

Combine like terms: 1 + -1 = 0
-2x = 0 + x2
-2x = x2

Solving
-2x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(2 + x) = 0

Ignore the factor -1.

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, -2}

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