-.5(32)*x^2+(320)*x+0=1000

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Solution for -.5(32)*x^2+(320)*x+0=1000 equation: 


Simplifying
-0.5(32) * x2 + (320) * x + 0 = 1000

Multiply -0.5 * 32
-16x2 + (320) * x + 0 = 1000

Reorder the terms:
0 + 320x + -16x2 = 1000
Remove the zero:
320x + -16x2 = 1000

Solving
320x + -16x2 = 1000

Solving for variable 'x'.

Reorder the terms:
-1000 + 320x + -16x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + 320x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-125 + 40x + -2x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-125 + 40x + -2x2)' equal to zero and attempt to solve:

Simplifying
-125 + 40x + -2x2 = 0

Solving
-125 + 40x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
62.5 + -20x + x2 = 0

Move the constant term to the right:

Add '-62.5' to each side of the equation.
62.5 + -20x + -62.5 + x2 = 0 + -62.5

Reorder the terms:
62.5 + -62.5 + -20x + x2 = 0 + -62.5

Combine like terms: 62.5 + -62.5 = 0.0
0.0 + -20x + x2 = 0 + -62.5
-20x + x2 = 0 + -62.5

Combine like terms: 0 + -62.5 = -62.5
-20x + x2 = -62.5

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -62.5 + 100

Reorder the terms:
100 + -20x + x2 = -62.5 + 100

Combine like terms: -62.5 + 100 = 37.5
100 + -20x + x2 = 37.5

Factor a perfect square on the left side:
(x + -10)(x + -10) = 37.5

Calculate the square root of the right side: 6.123724357

Break this problem into two subproblems by setting 
(x + -10) equal to 6.123724357 and -6.123724357.


Subproblem 1
x + -10 = 6.123724357

Simplifying
x + -10 = 6.123724357

Reorder the terms:
-10 + x = 6.123724357

Solving
-10 + x = 6.123724357

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 6.123724357 + 10

Combine like terms: -10 + 10 = 0
0 + x = 6.123724357 + 10
x = 6.123724357 + 10

Combine like terms: 6.123724357 + 10 = 16.123724357
x = 16.123724357

Simplifying
x = 16.123724357


Subproblem 2
x + -10 = -6.123724357

Simplifying
x + -10 = -6.123724357

Reorder the terms:
-10 + x = -6.123724357

Solving
-10 + x = -6.123724357

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -6.123724357 + 10

Combine like terms: -10 + 10 = 0
0 + x = -6.123724357 + 10
x = -6.123724357 + 10

Combine like terms: -6.123724357 + 10 = 3.876275643
x = 3.876275643

Simplifying
x = 3.876275643


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.123724357, 3.876275643}
Solution
x = {16.123724357, 3.876275643}

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