x^2-x+4=3x+1

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


Simplifying
x2 + -1x + 4 = 3x + 1

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

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

Solving
4 + -1x + x2 = 1 + 3x

Solving for variable 'x'.

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

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

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

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

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

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

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

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {1, 3}

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