x^2+4x+4=1600

Solution for x^2+4x+4=1600 equation:

Simplifying
x2 + 4x + 4 = 1600

Reorder the terms:
4 + 4x + x2 = 1600

Solving
4 + 4x + x2 = 1600

Solving for variable 'x'.

Reorder the terms:
4 + -1600 + 4x + x2 = 1600 + -1600

Combine like terms: 4 + -1600 = -1596
-1596 + 4x + x2 = 1600 + -1600

Combine like terms: 1600 + -1600 = 0
-1596 + 4x + x2 = 0

Factor a trinomial.
(-42 + -1x)(38 + -1x) = 0

Subproblem 1
Set the factor '(-42 + -1x)' equal to zero and attempt to solve:

Simplifying
-42 + -1x = 0

Solving
-42 + -1x = 0

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

Add '42' to each side of the equation.
-42 + 42 + -1x = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1x = 0 + 42
-1x = 0 + 42

Combine like terms: 0 + 42 = 42
-1x = 42

Divide each side by '-1'.
x = -42

Simplifying
x = -42
Subproblem 2
Set the factor '(38 + -1x)' equal to zero and attempt to solve:

Simplifying
38 + -1x = 0

Solving
38 + -1x = 0

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

Add '-38' to each side of the equation.
38 + -38 + -1x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + -1x = 0 + -38
-1x = 0 + -38

Combine like terms: 0 + -38 = -38
-1x = -38

Divide each side by '-1'.
x = 38

Simplifying
x = 38
Solution
x = {-42, 38}