10x^2+x+0.25=2.25

Solution for 10x^2+x+0.25=2.25 equation:

Simplifying
10x2 + x + 0.25 = 2.25

Reorder the terms:
0.25 + x + 10x2 = 2.25

Solving
0.25 + x + 10x2 = 2.25

Solving for variable 'x'.

Reorder the terms:
0.25 + -2.25 + x + 10x2 = 2.25 + -2.25

Combine like terms: 0.25 + -2.25 = -2
-2 + x + 10x2 = 2.25 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
-2 + x + 10x2 = 0.00

Factor a trinomial.
(-1 + -2x)(2 + -5x) = 0.00

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.5, 0.4}