x^2+3x+17=-7x+1

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Solution for x^2+3x+17=-7x+1 equation: 


Simplifying
x2 + 3x + 17 = -7x + 1

Reorder the terms:
17 + 3x + x2 = -7x + 1

Reorder the terms:
17 + 3x + x2 = 1 + -7x

Solving
17 + 3x + x2 = 1 + -7x

Solving for variable 'x'.

Reorder the terms:
17 + -1 + 3x + 7x + x2 = 1 + -7x + -1 + 7x

Combine like terms: 17 + -1 = 16
16 + 3x + 7x + x2 = 1 + -7x + -1 + 7x

Combine like terms: 3x + 7x = 10x
16 + 10x + x2 = 1 + -7x + -1 + 7x

Reorder the terms:
16 + 10x + x2 = 1 + -1 + -7x + 7x

Combine like terms: 1 + -1 = 0
16 + 10x + x2 = 0 + -7x + 7x
16 + 10x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
16 + 10x + x2 = 0

Factor a trinomial.
(8 + x)(2 + x) = 0


Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-8, -2}

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