3x^2=4x-1

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Solution for 3x^2=4x-1 equation:


Simplifying
3x2 = 4x + -1

Reorder the terms:
3x2 = -1 + 4x

Solving
3x2 = -1 + 4x

Solving for variable 'x'.

Reorder the terms:
1 + -4x + 3x2 = -1 + 4x + 1 + -4x

Reorder the terms:
1 + -4x + 3x2 = -1 + 1 + 4x + -4x

Combine like terms: -1 + 1 = 0
1 + -4x + 3x2 = 0 + 4x + -4x
1 + -4x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
1 + -4x + 3x2 = 0

Factor a trinomial.
(1 + -3x)(1 + -1x) = 0

Subproblem 1

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

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 = {0.3333333333, 1}

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