x^2-6.4x=-1.24

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Solution for x^2-6.4x=-1.24 equation: 


Simplifying
x2 + -6.4x = -1.24

Reorder the terms:
-6.4x + x2 = -1.24

Solving
-6.4x + x2 = -1.24

Solving for variable 'x'.

Reorder the terms:
1.24 + -6.4x + x2 = -1.24 + 1.24

Combine like terms: -1.24 + 1.24 = 0.00
1.24 + -6.4x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-1.24' to each side of the equation.
1.24 + -6.4x + -1.24 + x2 = 0.00 + -1.24

Reorder the terms:
1.24 + -1.24 + -6.4x + x2 = 0.00 + -1.24

Combine like terms: 1.24 + -1.24 = 0.00
0.00 + -6.4x + x2 = 0.00 + -1.24
-6.4x + x2 = 0.00 + -1.24

Combine like terms: 0.00 + -1.24 = -1.24
-6.4x + x2 = -1.24

The x term is -6.4x.  Take half its coefficient (-3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
-6.4x + 10.24 + x2 = -1.24 + 10.24

Reorder the terms:
10.24 + -6.4x + x2 = -1.24 + 10.24

Combine like terms: -1.24 + 10.24 = 9
10.24 + -6.4x + x2 = 9

Factor a perfect square on the left side:
(x + -3.2)(x + -3.2) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + -3.2) equal to 3 and -3.


Subproblem 1
x + -3.2 = 3

Simplifying
x + -3.2 = 3

Reorder the terms:
-3.2 + x = 3

Solving
-3.2 + x = 3

Solving for variable 'x'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + x = 3 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + x = 3 + 3.2
x = 3 + 3.2

Combine like terms: 3 + 3.2 = 6.2
x = 6.2

Simplifying
x = 6.2


Subproblem 2
x + -3.2 = -3

Simplifying
x + -3.2 = -3

Reorder the terms:
-3.2 + x = -3

Solving
-3.2 + x = -3

Solving for variable 'x'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + x = -3 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + x = -3 + 3.2
x = -3 + 3.2

Combine like terms: -3 + 3.2 = 0.2
x = 0.2

Simplifying
x = 0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.2, 0.2}

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