x^2+3x+1.25=5.25

Solution for x^2+3x+1.25=5.25 equation:

Simplifying
x2 + 3x + 1.25 = 5.25

Reorder the terms:
1.25 + 3x + x2 = 5.25

Solving
1.25 + 3x + x2 = 5.25

Solving for variable 'x'.

Reorder the terms:
1.25 + -5.25 + 3x + x2 = 5.25 + -5.25

Combine like terms: 1.25 + -5.25 = -4
-4 + 3x + x2 = 5.25 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
-4 + 3x + x2 = 0.00

Factor a trinomial.
(-4 + -1x)(1 + -1x) = 0.00

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}