-.5*32x^2+64x+0=-200

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Solution for -.5*32x^2+64x+0=-200 equation: 


Simplifying
-0.5 * 32x2 + 64x + 0 = -200

Multiply -0.5 * 32
-16x2 + 64x + 0 = -200

Reorder the terms:
0 + 64x + -16x2 = -200
Remove the zero:
64x + -16x2 = -200

Solving
64x + -16x2 = -200

Solving for variable 'x'.

Reorder the terms:
200 + 64x + -16x2 = -200 + 200

Combine like terms: -200 + 200 = 0
200 + 64x + -16x2 = 0

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

Ignore the factor 8.

Subproblem 1
Set the factor '(25 + 8x + -2x2)' equal to zero and attempt to solve:

Simplifying
25 + 8x + -2x2 = 0

Solving
25 + 8x + -2x2 = 0

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

Divide each side by '-2'.
-12.5 + -4x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -4x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -4x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -4x + x2 = 0 + 12.5
-4x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-4x + x2 = 12.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 12.5 + 4

Reorder the terms:
4 + -4x + x2 = 12.5 + 4

Combine like terms: 12.5 + 4 = 16.5
4 + -4x + x2 = 16.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 16.5

Calculate the square root of the right side: 4.062019202

Break this problem into two subproblems by setting 
(x + -2) equal to 4.062019202 and -4.062019202.


Subproblem 1
x + -2 = 4.062019202

Simplifying
x + -2 = 4.062019202

Reorder the terms:
-2 + x = 4.062019202

Solving
-2 + x = 4.062019202

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.062019202 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.062019202 + 2
x = 4.062019202 + 2

Combine like terms: 4.062019202 + 2 = 6.062019202
x = 6.062019202

Simplifying
x = 6.062019202


Subproblem 2
x + -2 = -4.062019202

Simplifying
x + -2 = -4.062019202

Reorder the terms:
-2 + x = -4.062019202

Solving
-2 + x = -4.062019202

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.062019202 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.062019202 + 2
x = -4.062019202 + 2

Combine like terms: -4.062019202 + 2 = -2.062019202
x = -2.062019202

Simplifying
x = -2.062019202


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.062019202, -2.062019202}
Solution
x = {6.062019202, -2.062019202}

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