x^2-5x+22=7x+2

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Solution for x^2-5x+22=7x+2 equation: 


Simplifying
x2 + -5x + 22 = 7x + 2

Reorder the terms:
22 + -5x + x2 = 7x + 2

Reorder the terms:
22 + -5x + x2 = 2 + 7x

Solving
22 + -5x + x2 = 2 + 7x

Solving for variable 'x'.

Reorder the terms:
22 + -2 + -5x + -7x + x2 = 2 + 7x + -2 + -7x

Combine like terms: 22 + -2 = 20
20 + -5x + -7x + x2 = 2 + 7x + -2 + -7x

Combine like terms: -5x + -7x = -12x
20 + -12x + x2 = 2 + 7x + -2 + -7x

Reorder the terms:
20 + -12x + x2 = 2 + -2 + 7x + -7x

Combine like terms: 2 + -2 = 0
20 + -12x + x2 = 0 + 7x + -7x
20 + -12x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
20 + -12x + x2 = 0

Factor a trinomial.
(2 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {2, 10}

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