x^2+13x+42.25=0.25

Solution for x^2+13x+42.25=0.25 equation:

Simplifying
x2 + 13x + 42.25 = 0.25

Reorder the terms:
42.25 + 13x + x2 = 0.25

Solving
42.25 + 13x + x2 = 0.25

Solving for variable 'x'.

Reorder the terms:
42.25 + -0.25 + 13x + x2 = 0.25 + -0.25

Combine like terms: 42.25 + -0.25 = 42
42 + 13x + x2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
42 + 13x + x2 = 0.00

Factor a trinomial.
(7 + x)(6 + x) = 0.00

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-7, -6}