2.67+5.67X+X^2=0

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Solution for 2.67+5.67X+X^2=0 equation: 


Simplifying
2.67 + 5.67X + X2 = 0

Solving
2.67 + 5.67X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-2.67' to each side of the equation.
2.67 + 5.67X + -2.67 + X2 = 0 + -2.67

Reorder the terms:
2.67 + -2.67 + 5.67X + X2 = 0 + -2.67

Combine like terms: 2.67 + -2.67 = 0.00
0.00 + 5.67X + X2 = 0 + -2.67
5.67X + X2 = 0 + -2.67

Combine like terms: 0 + -2.67 = -2.67
5.67X + X2 = -2.67

The X term is 5.67X.  Take half its coefficient (2.835).
Square it (8.037225) and add it to both sides.

Add '8.037225' to each side of the equation.
5.67X + 8.037225 + X2 = -2.67 + 8.037225

Reorder the terms:
8.037225 + 5.67X + X2 = -2.67 + 8.037225

Combine like terms: -2.67 + 8.037225 = 5.367225
8.037225 + 5.67X + X2 = 5.367225

Factor a perfect square on the left side:
(X + 2.835)(X + 2.835) = 5.367225

Calculate the square root of the right side: 2.316727217

Break this problem into two subproblems by setting 
(X + 2.835) equal to 2.316727217 and -2.316727217.


Subproblem 1
X + 2.835 = 2.316727217

Simplifying
X + 2.835 = 2.316727217

Reorder the terms:
2.835 + X = 2.316727217

Solving
2.835 + X = 2.316727217

Solving for variable 'X'.

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

Add '-2.835' to each side of the equation.
2.835 + -2.835 + X = 2.316727217 + -2.835

Combine like terms: 2.835 + -2.835 = 0.000
0.000 + X = 2.316727217 + -2.835
X = 2.316727217 + -2.835

Combine like terms: 2.316727217 + -2.835 = -0.518272783
X = -0.518272783

Simplifying
X = -0.518272783


Subproblem 2
X + 2.835 = -2.316727217

Simplifying
X + 2.835 = -2.316727217

Reorder the terms:
2.835 + X = -2.316727217

Solving
2.835 + X = -2.316727217

Solving for variable 'X'.

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

Add '-2.835' to each side of the equation.
2.835 + -2.835 + X = -2.316727217 + -2.835

Combine like terms: 2.835 + -2.835 = 0.000
0.000 + X = -2.316727217 + -2.835
X = -2.316727217 + -2.835

Combine like terms: -2.316727217 + -2.835 = -5.151727217
X = -5.151727217

Simplifying
X = -5.151727217


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.518272783, -5.151727217}

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