x^2+0.45x-0.17857=0

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Solution for x^2+0.45x-0.17857=0 equation:


Simplifying
x2 + 0.45x + -0.17857 = 0

Reorder the terms:
-0.17857 + 0.45x + x2 = 0

Solving
-0.17857 + 0.45x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.17857' to each side of the equation.
-0.17857 + 0.45x + 0.17857 + x2 = 0 + 0.17857

Reorder the terms:
-0.17857 + 0.17857 + 0.45x + x2 = 0 + 0.17857

Combine like terms: -0.17857 + 0.17857 = 0.00000
0.00000 + 0.45x + x2 = 0 + 0.17857
0.45x + x2 = 0 + 0.17857

Combine like terms: 0 + 0.17857 = 0.17857
0.45x + x2 = 0.17857

The x term is 0.45x.  Take half its coefficient (0.225).
Square it (0.050625) and add it to both sides.

Add '0.050625' to each side of the equation.
0.45x + 0.050625 + x2 = 0.17857 + 0.050625

Reorder the terms:
0.050625 + 0.45x + x2 = 0.17857 + 0.050625

Combine like terms: 0.17857 + 0.050625 = 0.229195
0.050625 + 0.45x + x2 = 0.229195

Factor a perfect square on the left side:
(x + 0.225)(x + 0.225) = 0.229195

Calculate the square root of the right side: 0.478743146

Break this problem into two subproblems by setting 
(x + 0.225) equal to 0.478743146 and -0.478743146.


Subproblem 1
x + 0.225 = 0.478743146

Simplifying
x + 0.225 = 0.478743146

Reorder the terms:
0.225 + x = 0.478743146

Solving
0.225 + x = 0.478743146

Solving for variable 'x'.

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

Add '-0.225' to each side of the equation.
0.225 + -0.225 + x = 0.478743146 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = 0.478743146 + -0.225
x = 0.478743146 + -0.225

Combine like terms: 0.478743146 + -0.225 = 0.253743146
x = 0.253743146

Simplifying
x = 0.253743146


Subproblem 2
x + 0.225 = -0.478743146

Simplifying
x + 0.225 = -0.478743146

Reorder the terms:
0.225 + x = -0.478743146

Solving
0.225 + x = -0.478743146

Solving for variable 'x'.

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

Add '-0.225' to each side of the equation.
0.225 + -0.225 + x = -0.478743146 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = -0.478743146 + -0.225
x = -0.478743146 + -0.225

Combine like terms: -0.478743146 + -0.225 = -0.703743146
x = -0.703743146

Simplifying
x = -0.703743146


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.253743146, -0.703743146}

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