0.09x^2-1.62x+4.05=0

Solution for 0.09x^2-1.62x+4.05=0 equation:

Simplifying
0.09x2 + -1.62x + 4.05 = 0

Reorder the terms:
4.05 + -1.62x + 0.09x2 = 0

Solving
4.05 + -1.62x + 0.09x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.09 the coefficient of the squared term: 

Divide each side by '0.09'.
45 + -18x + x2 = 0

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -18x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -18x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -18x + x2 = 0 + -45
-18x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-18x + x2 = -45

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -45 + 81

Reorder the terms:
81 + -18x + x2 = -45 + 81

Combine like terms: -45 + 81 = 36
81 + -18x + x2 = 36

Factor a perfect square on the left side:
(x + -9)(x + -9) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + -9) equal to 6 and -6.

Subproblem 1
x + -9 = 6

Simplifying
x + -9 = 6

Reorder the terms:
-9 + x = 6

Solving
-9 + x = 6

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 6 + 9

Combine like terms: -9 + 9 = 0
0 + x = 6 + 9
x = 6 + 9

Combine like terms: 6 + 9 = 15
x = 15

Simplifying
x = 15

Subproblem 2
x + -9 = -6

Simplifying
x + -9 = -6

Reorder the terms:
-9 + x = -6

Solving
-9 + x = -6

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -6 + 9

Combine like terms: -9 + 9 = 0
0 + x = -6 + 9
x = -6 + 9

Combine like terms: -6 + 9 = 3
x = 3

Simplifying
x = 3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15, 3}