-.5(32x^2)+1000x+50=0

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Solution for -.5(32x^2)+1000x+50=0 equation: 


Simplifying
-0.5(32x2) + 1000x + 50 = 0

Remove parenthesis around (32x2)
-0.5 * 32x2 + 1000x + 50 = 0

Multiply -0.5 * 32
-16x2 + 1000x + 50 = 0

Reorder the terms:
50 + 1000x + -16x2 = 0

Solving
50 + 1000x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 500x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 500x + -8x2)' equal to zero and attempt to solve:

Simplifying
25 + 500x + -8x2 = 0

Solving
25 + 500x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-3.125 + -62.5x + x2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -62.5x + 3.125 + x2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -62.5x + x2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -62.5x + x2 = 0 + 3.125
-62.5x + x2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-62.5x + x2 = 3.125

The x term is -62.5x.  Take half its coefficient (-31.25).
Square it (976.5625) and add it to both sides.

Add '976.5625' to each side of the equation.
-62.5x + 976.5625 + x2 = 3.125 + 976.5625

Reorder the terms:
976.5625 + -62.5x + x2 = 3.125 + 976.5625

Combine like terms: 3.125 + 976.5625 = 979.6875
976.5625 + -62.5x + x2 = 979.6875

Factor a perfect square on the left side:
(x + -31.25)(x + -31.25) = 979.6875

Calculate the square root of the right side: 31.299960064

Break this problem into two subproblems by setting 
(x + -31.25) equal to 31.299960064 and -31.299960064.


Subproblem 1
x + -31.25 = 31.299960064

Simplifying
x + -31.25 = 31.299960064

Reorder the terms:
-31.25 + x = 31.299960064

Solving
-31.25 + x = 31.299960064

Solving for variable 'x'.

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

Add '31.25' to each side of the equation.
-31.25 + 31.25 + x = 31.299960064 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + x = 31.299960064 + 31.25
x = 31.299960064 + 31.25

Combine like terms: 31.299960064 + 31.25 = 62.549960064
x = 62.549960064

Simplifying
x = 62.549960064


Subproblem 2
x + -31.25 = -31.299960064

Simplifying
x + -31.25 = -31.299960064

Reorder the terms:
-31.25 + x = -31.299960064

Solving
-31.25 + x = -31.299960064

Solving for variable 'x'.

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

Add '31.25' to each side of the equation.
-31.25 + 31.25 + x = -31.299960064 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + x = -31.299960064 + 31.25
x = -31.299960064 + 31.25

Combine like terms: -31.299960064 + 31.25 = -0.049960064
x = -0.049960064

Simplifying
x = -0.049960064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {62.549960064, -0.049960064}
Solution
x = {62.549960064, -0.049960064}

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