x^2+1.67x-5.3688=0

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Solution for x^2+1.67x-5.3688=0 equation: 


Simplifying
x2 + 1.67x + -5.3688 = 0

Reorder the terms:
-5.3688 + 1.67x + x2 = 0

Solving
-5.3688 + 1.67x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5.3688' to each side of the equation.
-5.3688 + 1.67x + 5.3688 + x2 = 0 + 5.3688

Reorder the terms:
-5.3688 + 5.3688 + 1.67x + x2 = 0 + 5.3688

Combine like terms: -5.3688 + 5.3688 = 0.0000
0.0000 + 1.67x + x2 = 0 + 5.3688
1.67x + x2 = 0 + 5.3688

Combine like terms: 0 + 5.3688 = 5.3688
1.67x + x2 = 5.3688

The x term is 1.67x.  Take half its coefficient (0.835).
Square it (0.697225) and add it to both sides.

Add '0.697225' to each side of the equation.
1.67x + 0.697225 + x2 = 5.3688 + 0.697225

Reorder the terms:
0.697225 + 1.67x + x2 = 5.3688 + 0.697225

Combine like terms: 5.3688 + 0.697225 = 6.066025
0.697225 + 1.67x + x2 = 6.066025

Factor a perfect square on the left side:
(x + 0.835)(x + 0.835) = 6.066025

Calculate the square root of the right side: 2.462930165

Break this problem into two subproblems by setting 
(x + 0.835) equal to 2.462930165 and -2.462930165.


Subproblem 1
x + 0.835 = 2.462930165

Simplifying
x + 0.835 = 2.462930165

Reorder the terms:
0.835 + x = 2.462930165

Solving
0.835 + x = 2.462930165

Solving for variable 'x'.

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

Add '-0.835' to each side of the equation.
0.835 + -0.835 + x = 2.462930165 + -0.835

Combine like terms: 0.835 + -0.835 = 0.000
0.000 + x = 2.462930165 + -0.835
x = 2.462930165 + -0.835

Combine like terms: 2.462930165 + -0.835 = 1.627930165
x = 1.627930165

Simplifying
x = 1.627930165


Subproblem 2
x + 0.835 = -2.462930165

Simplifying
x + 0.835 = -2.462930165

Reorder the terms:
0.835 + x = -2.462930165

Solving
0.835 + x = -2.462930165

Solving for variable 'x'.

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

Add '-0.835' to each side of the equation.
0.835 + -0.835 + x = -2.462930165 + -0.835

Combine like terms: 0.835 + -0.835 = 0.000
0.000 + x = -2.462930165 + -0.835
x = -2.462930165 + -0.835

Combine like terms: -2.462930165 + -0.835 = -3.297930165
x = -3.297930165

Simplifying
x = -3.297930165


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.627930165, -3.297930165}

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