.35x^2+2.3x-6.2=0

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Solution for .35x^2+2.3x-6.2=0 equation: 


Simplifying
0.35x2 + 2.3x + -6.2 = 0

Reorder the terms:
-6.2 + 2.3x + 0.35x2 = 0

Solving
-6.2 + 2.3x + 0.35x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.35'.
-17.71428571 + 6.571428571x + x2 = 0

Move the constant term to the right:

Add '17.71428571' to each side of the equation.
-17.71428571 + 6.571428571x + 17.71428571 + x2 = 0 + 17.71428571

Reorder the terms:
-17.71428571 + 17.71428571 + 6.571428571x + x2 = 0 + 17.71428571

Combine like terms: -17.71428571 + 17.71428571 = 0.00000000
0.00000000 + 6.571428571x + x2 = 0 + 17.71428571
6.571428571x + x2 = 0 + 17.71428571

Combine like terms: 0 + 17.71428571 = 17.71428571
6.571428571x + x2 = 17.71428571

The x term is 6.571428571x.  Take half its coefficient (3.285714286).
Square it (10.79591837) and add it to both sides.

Add '10.79591837' to each side of the equation.
6.571428571x + 10.79591837 + x2 = 17.71428571 + 10.79591837

Reorder the terms:
10.79591837 + 6.571428571x + x2 = 17.71428571 + 10.79591837

Combine like terms: 17.71428571 + 10.79591837 = 28.51020408
10.79591837 + 6.571428571x + x2 = 28.51020408

Factor a perfect square on the left side:
(x + 3.285714286)(x + 3.285714286) = 28.51020408

Calculate the square root of the right side: 5.33949474

Break this problem into two subproblems by setting 
(x + 3.285714286) equal to 5.33949474 and -5.33949474.


Subproblem 1
x + 3.285714286 = 5.33949474

Simplifying
x + 3.285714286 = 5.33949474

Reorder the terms:
3.285714286 + x = 5.33949474

Solving
3.285714286 + x = 5.33949474

Solving for variable 'x'.

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

Add '-3.285714286' to each side of the equation.
3.285714286 + -3.285714286 + x = 5.33949474 + -3.285714286

Combine like terms: 3.285714286 + -3.285714286 = 0.000000000
0.000000000 + x = 5.33949474 + -3.285714286
x = 5.33949474 + -3.285714286

Combine like terms: 5.33949474 + -3.285714286 = 2.053780454
x = 2.053780454

Simplifying
x = 2.053780454


Subproblem 2
x + 3.285714286 = -5.33949474

Simplifying
x + 3.285714286 = -5.33949474

Reorder the terms:
3.285714286 + x = -5.33949474

Solving
3.285714286 + x = -5.33949474

Solving for variable 'x'.

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

Add '-3.285714286' to each side of the equation.
3.285714286 + -3.285714286 + x = -5.33949474 + -3.285714286

Combine like terms: 3.285714286 + -3.285714286 = 0.000000000
0.000000000 + x = -5.33949474 + -3.285714286
x = -5.33949474 + -3.285714286

Combine like terms: -5.33949474 + -3.285714286 = -8.625209026
x = -8.625209026

Simplifying
x = -8.625209026


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.053780454, -8.625209026}

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