x^2+1.8x-0.225=0

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Solution for x^2+1.8x-0.225=0 equation: 


Simplifying
x2 + 1.8x + -0.225 = 0

Reorder the terms:
-0.225 + 1.8x + x2 = 0

Solving
-0.225 + 1.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.225' to each side of the equation.
-0.225 + 1.8x + 0.225 + x2 = 0 + 0.225

Reorder the terms:
-0.225 + 0.225 + 1.8x + x2 = 0 + 0.225

Combine like terms: -0.225 + 0.225 = 0.000
0.000 + 1.8x + x2 = 0 + 0.225
1.8x + x2 = 0 + 0.225

Combine like terms: 0 + 0.225 = 0.225
1.8x + x2 = 0.225

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 0.225 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 0.225 + 0.81

Combine like terms: 0.225 + 0.81 = 1.035
0.81 + 1.8x + x2 = 1.035

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 1.035

Calculate the square root of the right side: 1.017349497

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.017349497 and -1.017349497.


Subproblem 1
x + 0.9 = 1.017349497

Simplifying
x + 0.9 = 1.017349497

Reorder the terms:
0.9 + x = 1.017349497

Solving
0.9 + x = 1.017349497

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 1.017349497 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 1.017349497 + -0.9
x = 1.017349497 + -0.9

Combine like terms: 1.017349497 + -0.9 = 0.117349497
x = 0.117349497

Simplifying
x = 0.117349497


Subproblem 2
x + 0.9 = -1.017349497

Simplifying
x + 0.9 = -1.017349497

Reorder the terms:
0.9 + x = -1.017349497

Solving
0.9 + x = -1.017349497

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -1.017349497 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -1.017349497 + -0.9
x = -1.017349497 + -0.9

Combine like terms: -1.017349497 + -0.9 = -1.917349497
x = -1.917349497

Simplifying
x = -1.917349497


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.117349497, -1.917349497}

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