x^2-3x-34=1-5x

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Solution for x^2-3x-34=1-5x equation:


Simplifying
x2 + -3x + -34 = 1 + -5x

Reorder the terms:
-34 + -3x + x2 = 1 + -5x

Solving
-34 + -3x + x2 = 1 + -5x

Solving for variable 'x'.

Reorder the terms:
-34 + -1 + -3x + 5x + x2 = 1 + -5x + -1 + 5x

Combine like terms: -34 + -1 = -35
-35 + -3x + 5x + x2 = 1 + -5x + -1 + 5x

Combine like terms: -3x + 5x = 2x
-35 + 2x + x2 = 1 + -5x + -1 + 5x

Reorder the terms:
-35 + 2x + x2 = 1 + -1 + -5x + 5x

Combine like terms: 1 + -1 = 0
-35 + 2x + x2 = 0 + -5x + 5x
-35 + 2x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-35 + 2x + x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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