16x^2+120x-200=0

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Solution for 16x^2+120x-200=0 equation: 


Simplifying
16x2 + 120x + -200 = 0

Reorder the terms:
-200 + 120x + 16x2 = 0

Solving
-200 + 120x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-25 + 15x + 2x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-25 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-25 + 15x + 2x2 = 0

Solving
-25 + 15x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + 7.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 7.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 7.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 7.5x + x2 = 0 + 12.5
7.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
7.5x + x2 = 12.5

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 12.5 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 12.5 + 14.0625

Combine like terms: 12.5 + 14.0625 = 26.5625
14.0625 + 7.5x + x2 = 26.5625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 26.5625

Calculate the square root of the right side: 5.153882032

Break this problem into two subproblems by setting 
(x + 3.75) equal to 5.153882032 and -5.153882032.


Subproblem 1
x + 3.75 = 5.153882032

Simplifying
x + 3.75 = 5.153882032

Reorder the terms:
3.75 + x = 5.153882032

Solving
3.75 + x = 5.153882032

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 5.153882032 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 5.153882032 + -3.75
x = 5.153882032 + -3.75

Combine like terms: 5.153882032 + -3.75 = 1.403882032
x = 1.403882032

Simplifying
x = 1.403882032


Subproblem 2
x + 3.75 = -5.153882032

Simplifying
x + 3.75 = -5.153882032

Reorder the terms:
3.75 + x = -5.153882032

Solving
3.75 + x = -5.153882032

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -5.153882032 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -5.153882032 + -3.75
x = -5.153882032 + -3.75

Combine like terms: -5.153882032 + -3.75 = -8.903882032
x = -8.903882032

Simplifying
x = -8.903882032


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.403882032, -8.903882032}
Solution
x = {1.403882032, -8.903882032}

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