16x^2+1100x-6050=0

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Solution for 16x^2+1100x-6050=0 equation: 


Simplifying
16x2 + 1100x + -6050 = 0

Reorder the terms:
-6050 + 1100x + 16x2 = 0

Solving
-6050 + 1100x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3025 + 550x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3025 + 550x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3025 + 550x + 8x2 = 0

Solving
-3025 + 550x + 8x2 = 0

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

Divide each side by '8'.
-378.125 + 68.75x + x2 = 0

Move the constant term to the right:

Add '378.125' to each side of the equation.
-378.125 + 68.75x + 378.125 + x2 = 0 + 378.125

Reorder the terms:
-378.125 + 378.125 + 68.75x + x2 = 0 + 378.125

Combine like terms: -378.125 + 378.125 = 0.000
0.000 + 68.75x + x2 = 0 + 378.125
68.75x + x2 = 0 + 378.125

Combine like terms: 0 + 378.125 = 378.125
68.75x + x2 = 378.125

The x term is 68.75x.  Take half its coefficient (34.375).
Square it (1181.640625) and add it to both sides.

Add '1181.640625' to each side of the equation.
68.75x + 1181.640625 + x2 = 378.125 + 1181.640625

Reorder the terms:
1181.640625 + 68.75x + x2 = 378.125 + 1181.640625

Combine like terms: 378.125 + 1181.640625 = 1559.765625
1181.640625 + 68.75x + x2 = 1559.765625

Factor a perfect square on the left side:
(x + 34.375)(x + 34.375) = 1559.765625

Calculate the square root of the right side: 39.493868195

Break this problem into two subproblems by setting 
(x + 34.375) equal to 39.493868195 and -39.493868195.


Subproblem 1
x + 34.375 = 39.493868195

Simplifying
x + 34.375 = 39.493868195

Reorder the terms:
34.375 + x = 39.493868195

Solving
34.375 + x = 39.493868195

Solving for variable 'x'.

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

Add '-34.375' to each side of the equation.
34.375 + -34.375 + x = 39.493868195 + -34.375

Combine like terms: 34.375 + -34.375 = 0.000
0.000 + x = 39.493868195 + -34.375
x = 39.493868195 + -34.375

Combine like terms: 39.493868195 + -34.375 = 5.118868195
x = 5.118868195

Simplifying
x = 5.118868195


Subproblem 2
x + 34.375 = -39.493868195

Simplifying
x + 34.375 = -39.493868195

Reorder the terms:
34.375 + x = -39.493868195

Solving
34.375 + x = -39.493868195

Solving for variable 'x'.

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

Add '-34.375' to each side of the equation.
34.375 + -34.375 + x = -39.493868195 + -34.375

Combine like terms: 34.375 + -34.375 = 0.000
0.000 + x = -39.493868195 + -34.375
x = -39.493868195 + -34.375

Combine like terms: -39.493868195 + -34.375 = -73.868868195
x = -73.868868195

Simplifying
x = -73.868868195


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.118868195, -73.868868195}
Solution
x = {5.118868195, -73.868868195}

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