685=2x^2+2x+1

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Solution for 685=2x^2+2x+1 equation: 


Simplifying
685 = 2x2 + 2x + 1

Reorder the terms:
685 = 1 + 2x + 2x2

Solving
685 = 1 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 685 + -1 = 684
684 + -2x + -2x2 = 1 + 2x + 2x2 + -1 + -2x + -2x2

Reorder the terms:
684 + -2x + -2x2 = 1 + -1 + 2x + -2x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
684 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
684 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
684 + -2x + -2x2 = 0 + 2x2 + -2x2
684 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
684 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(342 + -1x + -1x2) = 0

Factor a trinomial.
2((18 + -1x)(19 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18

Subproblem 2
Set the factor '(19 + x)' equal to zero and attempt to solve:

Simplifying
19 + x = 0

Solving
19 + x = 0

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

Add '-19' to each side of the equation.
19 + -19 + x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + x = 0 + -19
x = 0 + -19

Combine like terms: 0 + -19 = -19
x = -19

Simplifying
x = -19
Solution
x = {18, -19}

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