x^2+0.755x-0.177=0

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Solution for x^2+0.755x-0.177=0 equation: 


Simplifying
x2 + 0.755x + -0.177 = 0

Reorder the terms:
-0.177 + 0.755x + x2 = 0

Solving
-0.177 + 0.755x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.177' to each side of the equation.
-0.177 + 0.755x + 0.177 + x2 = 0 + 0.177

Reorder the terms:
-0.177 + 0.177 + 0.755x + x2 = 0 + 0.177

Combine like terms: -0.177 + 0.177 = 0.000
0.000 + 0.755x + x2 = 0 + 0.177
0.755x + x2 = 0 + 0.177

Combine like terms: 0 + 0.177 = 0.177
0.755x + x2 = 0.177

The x term is 0.755x.  Take half its coefficient (0.3775).
Square it (0.14250625) and add it to both sides.

Add '0.14250625' to each side of the equation.
0.755x + 0.14250625 + x2 = 0.177 + 0.14250625

Reorder the terms:
0.14250625 + 0.755x + x2 = 0.177 + 0.14250625

Combine like terms: 0.177 + 0.14250625 = 0.31950625
0.14250625 + 0.755x + x2 = 0.31950625

Factor a perfect square on the left side:
(x + 0.3775)(x + 0.3775) = 0.31950625

Calculate the square root of the right side: 0.565248839

Break this problem into two subproblems by setting 
(x + 0.3775) equal to 0.565248839 and -0.565248839.


Subproblem 1
x + 0.3775 = 0.565248839

Simplifying
x + 0.3775 = 0.565248839

Reorder the terms:
0.3775 + x = 0.565248839

Solving
0.3775 + x = 0.565248839

Solving for variable 'x'.

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

Add '-0.3775' to each side of the equation.
0.3775 + -0.3775 + x = 0.565248839 + -0.3775

Combine like terms: 0.3775 + -0.3775 = 0.0000
0.0000 + x = 0.565248839 + -0.3775
x = 0.565248839 + -0.3775

Combine like terms: 0.565248839 + -0.3775 = 0.187748839
x = 0.187748839

Simplifying
x = 0.187748839


Subproblem 2
x + 0.3775 = -0.565248839

Simplifying
x + 0.3775 = -0.565248839

Reorder the terms:
0.3775 + x = -0.565248839

Solving
0.3775 + x = -0.565248839

Solving for variable 'x'.

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

Add '-0.3775' to each side of the equation.
0.3775 + -0.3775 + x = -0.565248839 + -0.3775

Combine like terms: 0.3775 + -0.3775 = 0.0000
0.0000 + x = -0.565248839 + -0.3775
x = -0.565248839 + -0.3775

Combine like terms: -0.565248839 + -0.3775 = -0.942748839
x = -0.942748839

Simplifying
x = -0.942748839


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.187748839, -0.942748839}

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