x^2-6.2x-6.2=0

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Solution for x^2-6.2x-6.2=0 equation: 


Simplifying
x2 + -6.2x + -6.2 = 0

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

Solving
-6.2 + -6.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6.2' to each side of the equation.
-6.2 + -6.2x + 6.2 + x2 = 0 + 6.2

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

Combine like terms: -6.2 + 6.2 = 0.0
0.0 + -6.2x + x2 = 0 + 6.2
-6.2x + x2 = 0 + 6.2

Combine like terms: 0 + 6.2 = 6.2
-6.2x + x2 = 6.2

The x term is -6.2x.  Take half its coefficient (-3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
-6.2x + 9.61 + x2 = 6.2 + 9.61

Reorder the terms:
9.61 + -6.2x + x2 = 6.2 + 9.61

Combine like terms: 6.2 + 9.61 = 15.81
9.61 + -6.2x + x2 = 15.81

Factor a perfect square on the left side:
(x + -3.1)(x + -3.1) = 15.81

Calculate the square root of the right side: 3.97617907

Break this problem into two subproblems by setting 
(x + -3.1) equal to 3.97617907 and -3.97617907.


Subproblem 1
x + -3.1 = 3.97617907

Simplifying
x + -3.1 = 3.97617907

Reorder the terms:
-3.1 + x = 3.97617907

Solving
-3.1 + x = 3.97617907

Solving for variable 'x'.

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

Add '3.1' to each side of the equation.
-3.1 + 3.1 + x = 3.97617907 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + x = 3.97617907 + 3.1
x = 3.97617907 + 3.1

Combine like terms: 3.97617907 + 3.1 = 7.07617907
x = 7.07617907

Simplifying
x = 7.07617907


Subproblem 2
x + -3.1 = -3.97617907

Simplifying
x + -3.1 = -3.97617907

Reorder the terms:
-3.1 + x = -3.97617907

Solving
-3.1 + x = -3.97617907

Solving for variable 'x'.

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

Add '3.1' to each side of the equation.
-3.1 + 3.1 + x = -3.97617907 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + x = -3.97617907 + 3.1
x = -3.97617907 + 3.1

Combine like terms: -3.97617907 + 3.1 = -0.87617907
x = -0.87617907

Simplifying
x = -0.87617907


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.07617907, -0.87617907}

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