x^2-6.2x-21.7=0

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Solution for x^2-6.2x-21.7=0 equation: 


Simplifying
x2 + -6.2x + -21.7 = 0

Reorder the terms:
-21.7 + -6.2x + x2 = 0

Solving
-21.7 + -6.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21.7' to each side of the equation.
-21.7 + -6.2x + 21.7 + x2 = 0 + 21.7

Reorder the terms:
-21.7 + 21.7 + -6.2x + x2 = 0 + 21.7

Combine like terms: -21.7 + 21.7 = 0.0
0.0 + -6.2x + x2 = 0 + 21.7
-6.2x + x2 = 0 + 21.7

Combine like terms: 0 + 21.7 = 21.7
-6.2x + x2 = 21.7

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 = 21.7 + 9.61

Reorder the terms:
9.61 + -6.2x + x2 = 21.7 + 9.61

Combine like terms: 21.7 + 9.61 = 31.31
9.61 + -6.2x + x2 = 31.31

Factor a perfect square on the left side:
(x + -3.1)(x + -3.1) = 31.31

Calculate the square root of the right side: 5.595533933

Break this problem into two subproblems by setting 
(x + -3.1) equal to 5.595533933 and -5.595533933.


Subproblem 1
x + -3.1 = 5.595533933

Simplifying
x + -3.1 = 5.595533933

Reorder the terms:
-3.1 + x = 5.595533933

Solving
-3.1 + x = 5.595533933

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 = 5.595533933 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + x = 5.595533933 + 3.1
x = 5.595533933 + 3.1

Combine like terms: 5.595533933 + 3.1 = 8.695533933
x = 8.695533933

Simplifying
x = 8.695533933


Subproblem 2
x + -3.1 = -5.595533933

Simplifying
x + -3.1 = -5.595533933

Reorder the terms:
-3.1 + x = -5.595533933

Solving
-3.1 + x = -5.595533933

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 = -5.595533933 + 3.1

Combine like terms: -3.1 + 3.1 = 0.0
0.0 + x = -5.595533933 + 3.1
x = -5.595533933 + 3.1

Combine like terms: -5.595533933 + 3.1 = -2.495533933
x = -2.495533933

Simplifying
x = -2.495533933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.695533933, -2.495533933}

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