-.5x^2+12.5x+1.6=0

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Solution for -.5x^2+12.5x+1.6=0 equation: 


Simplifying
-0.5x2 + 12.5x + 1.6 = 0

Reorder the terms:
1.6 + 12.5x + -0.5x2 = 0

Solving
1.6 + 12.5x + -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'.
-3.2 + -25x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -25x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -25x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -25x + x2 = 0 + 3.2
-25x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-25x + x2 = 3.2

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = 3.2 + 156.25

Reorder the terms:
156.25 + -25x + x2 = 3.2 + 156.25

Combine like terms: 3.2 + 156.25 = 159.45
156.25 + -25x + x2 = 159.45

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 159.45

Calculate the square root of the right side: 12.627351266

Break this problem into two subproblems by setting 
(x + -12.5) equal to 12.627351266 and -12.627351266.


Subproblem 1
x + -12.5 = 12.627351266

Simplifying
x + -12.5 = 12.627351266

Reorder the terms:
-12.5 + x = 12.627351266

Solving
-12.5 + x = 12.627351266

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 12.627351266 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 12.627351266 + 12.5
x = 12.627351266 + 12.5

Combine like terms: 12.627351266 + 12.5 = 25.127351266
x = 25.127351266

Simplifying
x = 25.127351266


Subproblem 2
x + -12.5 = -12.627351266

Simplifying
x + -12.5 = -12.627351266

Reorder the terms:
-12.5 + x = -12.627351266

Solving
-12.5 + x = -12.627351266

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -12.627351266 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -12.627351266 + 12.5
x = -12.627351266 + 12.5

Combine like terms: -12.627351266 + 12.5 = -0.127351266
x = -0.127351266

Simplifying
x = -0.127351266


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.127351266, -0.127351266}

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