2x(x-1)-x+1=0

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Solution for 2x(x-1)-x+1=0 equation:


Simplifying
2x(x + -1) + -1x + 1 = 0

Reorder the terms:
2x(-1 + x) + -1x + 1 = 0
(-1 * 2x + x * 2x) + -1x + 1 = 0
(-2x + 2x2) + -1x + 1 = 0

Reorder the terms:
1 + -2x + -1x + 2x2 = 0

Combine like terms: -2x + -1x = -3x
1 + -3x + 2x2 = 0

Solving
1 + -3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(1 + -1x) = 0

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

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 = {0.5, 1}

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