x^2+.45x-0.115=0

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Solution for x^2+.45x-0.115=0 equation: 


Simplifying
x2 + 0.45x + -0.115 = 0

Reorder the terms:
-0.115 + 0.45x + x2 = 0

Solving
-0.115 + 0.45x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.115' to each side of the equation.
-0.115 + 0.45x + 0.115 + x2 = 0 + 0.115

Reorder the terms:
-0.115 + 0.115 + 0.45x + x2 = 0 + 0.115

Combine like terms: -0.115 + 0.115 = 0.000
0.000 + 0.45x + x2 = 0 + 0.115
0.45x + x2 = 0 + 0.115

Combine like terms: 0 + 0.115 = 0.115
0.45x + x2 = 0.115

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 = 0.115 + 0.050625

Reorder the terms:
0.050625 + 0.45x + x2 = 0.115 + 0.050625

Combine like terms: 0.115 + 0.050625 = 0.165625
0.050625 + 0.45x + x2 = 0.165625

Factor a perfect square on the left side:
(x + 0.225)(x + 0.225) = 0.165625

Calculate the square root of the right side: 0.406970515

Break this problem into two subproblems by setting 
(x + 0.225) equal to 0.406970515 and -0.406970515.


Subproblem 1
x + 0.225 = 0.406970515

Simplifying
x + 0.225 = 0.406970515

Reorder the terms:
0.225 + x = 0.406970515

Solving
0.225 + x = 0.406970515

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 = 0.406970515 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = 0.406970515 + -0.225
x = 0.406970515 + -0.225

Combine like terms: 0.406970515 + -0.225 = 0.181970515
x = 0.181970515

Simplifying
x = 0.181970515


Subproblem 2
x + 0.225 = -0.406970515

Simplifying
x + 0.225 = -0.406970515

Reorder the terms:
0.225 + x = -0.406970515

Solving
0.225 + x = -0.406970515

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 = -0.406970515 + -0.225

Combine like terms: 0.225 + -0.225 = 0.000
0.000 + x = -0.406970515 + -0.225
x = -0.406970515 + -0.225

Combine like terms: -0.406970515 + -0.225 = -0.631970515
x = -0.631970515

Simplifying
x = -0.631970515


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.181970515, -0.631970515}

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