4x^2=4x-1

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Solution for 4x^2=4x-1 equation:


Simplifying
4x2 = 4x + -1

Reorder the terms:
4x2 = -1 + 4x

Solving
4x2 = -1 + 4x

Solving for variable 'x'.

Reorder the terms:
1 + -4x + 4x2 = -1 + 4x + 1 + -4x

Reorder the terms:
1 + -4x + 4x2 = -1 + 1 + 4x + -4x

Combine like terms: -1 + 1 = 0
1 + -4x + 4x2 = 0 + 4x + -4x
1 + -4x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -4x + 4x2 = 0

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

Solution

x = {0.5, 0.5}

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