x^2+x+0.5=1332+0.5

Solution for x^2+x+0.5=1332+0.5 equation:

Simplifying
x2 + x + 0.5 = 1332 + 0.5

Reorder the terms:
0.5 + x + x2 = 1332 + 0.5

Combine like terms: 1332 + 0.5 = 1332.5
0.5 + x + x2 = 1332.5

Solving
0.5 + x + x2 = 1332.5

Solving for variable 'x'.

Reorder the terms:
0.5 + -1332.5 + x + x2 = 1332.5 + -1332.5

Combine like terms: 0.5 + -1332.5 = -1332
-1332 + x + x2 = 1332.5 + -1332.5

Combine like terms: 1332.5 + -1332.5 = 0.0
-1332 + x + x2 = 0.0

Factor a trinomial.
(-37 + -1x)(36 + -1x) = 0.0

Subproblem 1
Set the factor '(-37 + -1x)' equal to zero and attempt to solve:

Simplifying
-37 + -1x = 0

Solving
-37 + -1x = 0

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

Add '37' to each side of the equation.
-37 + 37 + -1x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -1x = 0 + 37
-1x = 0 + 37

Combine like terms: 0 + 37 = 37
-1x = 37

Divide each side by '-1'.
x = -37

Simplifying
x = -37
Subproblem 2
Set the factor '(36 + -1x)' equal to zero and attempt to solve:

Simplifying
36 + -1x = 0

Solving
36 + -1x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -1x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -1x = 0 + -36
-1x = 0 + -36

Combine like terms: 0 + -36 = -36
-1x = -36

Divide each side by '-1'.
x = 36

Simplifying
x = 36
Solution
x = {-37, 36}