x^2+2x+1=400

Solution for x^2+2x+1=400 equation:

Simplifying
x2 + 2x + 1 = 400

Reorder the terms:
1 + 2x + x2 = 400

Solving
1 + 2x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
1 + -400 + 2x + x2 = 400 + -400

Combine like terms: 1 + -400 = -399
-399 + 2x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-399 + 2x + x2 = 0

Factor a trinomial.
(-21 + -1x)(19 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = 0 + 21
-1x = 0 + 21

Combine like terms: 0 + 21 = 21
-1x = 21

Divide each side by '-1'.
x = -21

Simplifying
x = -21
Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 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 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-21, 19}