x^2-7x-17=2x+5

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Solution for x^2-7x-17=2x+5 equation: 


Simplifying
x2 + -7x + -17 = 2x + 5

Reorder the terms:
-17 + -7x + x2 = 2x + 5

Reorder the terms:
-17 + -7x + x2 = 5 + 2x

Solving
-17 + -7x + x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
-17 + -5 + -7x + -2x + x2 = 5 + 2x + -5 + -2x

Combine like terms: -17 + -5 = -22
-22 + -7x + -2x + x2 = 5 + 2x + -5 + -2x

Combine like terms: -7x + -2x = -9x
-22 + -9x + x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-22 + -9x + x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-22 + -9x + x2 = 0 + 2x + -2x
-22 + -9x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-22 + -9x + x2 = 0

Factor a trinomial.
(-2 + -1x)(11 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-2, 11}

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