.5x^2-5x+8=0

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Solution for .5x^2-5x+8=0 equation: 


Simplifying
0.5x2 + -5x + 8 = 0

Reorder the terms:
8 + -5x + 0.5x2 = 0

Solving
8 + -5x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
16 + -10x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -10x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -10x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -10x + x2 = 0 + -16
-10x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-10x + x2 = -16

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -16 + 25

Reorder the terms:
25 + -10x + x2 = -16 + 25

Combine like terms: -16 + 25 = 9
25 + -10x + x2 = 9

Factor a perfect square on the left side:
(x + -5)(x + -5) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + -5) equal to 3 and -3.


Subproblem 1
x + -5 = 3

Simplifying
x + -5 = 3

Reorder the terms:
-5 + x = 3

Solving
-5 + x = 3

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3 + 5
x = 3 + 5

Combine like terms: 3 + 5 = 8
x = 8

Simplifying
x = 8


Subproblem 2
x + -5 = -3

Simplifying
x + -5 = -3

Reorder the terms:
-5 + x = -3

Solving
-5 + x = -3

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3 + 5
x = -3 + 5

Combine like terms: -3 + 5 = 2
x = 2

Simplifying
x = 2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8, 2}

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