4x=3x^2+1

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


Simplifying
4x = 3x2 + 1

Reorder the terms:
4x = 1 + 3x2

Solving
4x = 1 + 3x2

Solving for variable 'x'.

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

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

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

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

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

Solution

x = {1, 0.3333333333}

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