x^2+3x+2.25=42.25

Solution for x^2+3x+2.25=42.25 equation:

Simplifying
x2 + 3x + 2.25 = 42.25

Reorder the terms:
2.25 + 3x + x2 = 42.25

Solving
2.25 + 3x + x2 = 42.25

Solving for variable 'x'.

Reorder the terms:
2.25 + -42.25 + 3x + x2 = 42.25 + -42.25

Combine like terms: 2.25 + -42.25 = -40
-40 + 3x + x2 = 42.25 + -42.25

Combine like terms: 42.25 + -42.25 = 0.00
-40 + 3x + x2 = 0.00

Factor a trinomial.
(-8 + -1x)(5 + -1x) = 0.00

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 5}