-0.2x^2+1.3x+6.2=0

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Solution for -0.2x^2+1.3x+6.2=0 equation: 


Simplifying
-0.2x2 + 1.3x + 6.2 = 0

Reorder the terms:
6.2 + 1.3x + -0.2x2 = 0

Solving
6.2 + 1.3x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-31 + -6.5x + x2 = 0

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -6.5x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -6.5x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -6.5x + x2 = 0 + 31
-6.5x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-6.5x + x2 = 31

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 31 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 31 + 10.5625

Combine like terms: 31 + 10.5625 = 41.5625
10.5625 + -6.5x + x2 = 41.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(x + -3.25) equal to 6.446898479 and -6.446898479.


Subproblem 1
x + -3.25 = 6.446898479

Simplifying
x + -3.25 = 6.446898479

Reorder the terms:
-3.25 + x = 6.446898479

Solving
-3.25 + x = 6.446898479

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 6.446898479 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 6.446898479 + 3.25
x = 6.446898479 + 3.25

Combine like terms: 6.446898479 + 3.25 = 9.696898479
x = 9.696898479

Simplifying
x = 9.696898479


Subproblem 2
x + -3.25 = -6.446898479

Simplifying
x + -3.25 = -6.446898479

Reorder the terms:
-3.25 + x = -6.446898479

Solving
-3.25 + x = -6.446898479

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -6.446898479 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -6.446898479 + 3.25
x = -6.446898479 + 3.25

Combine like terms: -6.446898479 + 3.25 = -3.196898479
x = -3.196898479

Simplifying
x = -3.196898479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.696898479, -3.196898479}

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