2*X*X+6X-5=0

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Solution for 2*X*X+6X-5=0 equation: 


Simplifying
2X * X + 6X + -5 = 0

Multiply X * X
2X2 + 6X + -5 = 0

Reorder the terms:
-5 + 6X + 2X2 = 0

Solving
-5 + 6X + 2X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.5 + 3X + X2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3X + 2.5 + X2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3X + X2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3X + X2 = 0 + 2.5
3X + X2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3X + X2 = 2.5

The X term is 3X.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3X + 2.25 + X2 = 2.5 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 2.5 + 2.25

Combine like terms: 2.5 + 2.25 = 4.75
2.25 + 3X + X2 = 4.75

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(X + 1.5) equal to 2.179449472 and -2.179449472.


Subproblem 1
X + 1.5 = 2.179449472

Simplifying
X + 1.5 = 2.179449472

Reorder the terms:
1.5 + X = 2.179449472

Solving
1.5 + X = 2.179449472

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = 2.179449472 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = 2.179449472 + -1.5
X = 2.179449472 + -1.5

Combine like terms: 2.179449472 + -1.5 = 0.679449472
X = 0.679449472

Simplifying
X = 0.679449472


Subproblem 2
X + 1.5 = -2.179449472

Simplifying
X + 1.5 = -2.179449472

Reorder the terms:
1.5 + X = -2.179449472

Solving
1.5 + X = -2.179449472

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = -2.179449472 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = -2.179449472 + -1.5
X = -2.179449472 + -1.5

Combine like terms: -2.179449472 + -1.5 = -3.679449472
X = -3.679449472

Simplifying
X = -3.679449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.679449472, -3.679449472}

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