-x^2=1-2x

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


Simplifying
-1x2 = 1 + -2x

Solving
-1x2 = 1 + -2x

Solving for variable 'x'.

Reorder the terms:
-1 + 2x + -1x2 = 1 + -2x + -1 + 2x

Reorder the terms:
-1 + 2x + -1x2 = 1 + -1 + -2x + 2x

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

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

Factor a trinomial.
(-1 + x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1

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 = {1, 1}

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