x^2+x+.25=30.25

Solution for x^2+x+.25=30.25 equation:

Simplifying
x2 + x + 0.25 = 30.25

Reorder the terms:
0.25 + x + x2 = 30.25

Solving
0.25 + x + x2 = 30.25

Solving for variable 'x'.

Reorder the terms:
0.25 + -30.25 + x + x2 = 30.25 + -30.25

Combine like terms: 0.25 + -30.25 = -30
-30 + x + x2 = 30.25 + -30.25

Combine like terms: 30.25 + -30.25 = 0.00
-30 + x + x2 = 0.00

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 0.00

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}