x^2-8x+6.2=0

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Solution for x^2-8x+6.2=0 equation: 


Simplifying
x2 + -8x + 6.2 = 0

Reorder the terms:
6.2 + -8x + x2 = 0

Solving
6.2 + -8x + 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 + -8x + -6.2 + x2 = 0 + -6.2

Reorder the terms:
6.2 + -6.2 + -8x + x2 = 0 + -6.2

Combine like terms: 6.2 + -6.2 = 0.0
0.0 + -8x + x2 = 0 + -6.2
-8x + x2 = 0 + -6.2

Combine like terms: 0 + -6.2 = -6.2
-8x + x2 = -6.2

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -6.2 + 16

Reorder the terms:
16 + -8x + x2 = -6.2 + 16

Combine like terms: -6.2 + 16 = 9.8
16 + -8x + x2 = 9.8

Factor a perfect square on the left side:
(x + -4)(x + -4) = 9.8

Calculate the square root of the right side: 3.130495169

Break this problem into two subproblems by setting 
(x + -4) equal to 3.130495169 and -3.130495169.


Subproblem 1
x + -4 = 3.130495169

Simplifying
x + -4 = 3.130495169

Reorder the terms:
-4 + x = 3.130495169

Solving
-4 + x = 3.130495169

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.130495169 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.130495169 + 4
x = 3.130495169 + 4

Combine like terms: 3.130495169 + 4 = 7.130495169
x = 7.130495169

Simplifying
x = 7.130495169


Subproblem 2
x + -4 = -3.130495169

Simplifying
x + -4 = -3.130495169

Reorder the terms:
-4 + x = -3.130495169

Solving
-4 + x = -3.130495169

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.130495169 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.130495169 + 4
x = -3.130495169 + 4

Combine like terms: -3.130495169 + 4 = 0.869504831
x = 0.869504831

Simplifying
x = 0.869504831


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.130495169, 0.869504831}

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