2x^2+56x-1950=0

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Solution for 2x^2+56x-1950=0 equation: 


Simplifying
2x2 + 56x + -1950 = 0

Reorder the terms:
-1950 + 56x + 2x2 = 0

Solving
-1950 + 56x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-975 + 28x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-975 + 28x + x2)' equal to zero and attempt to solve:

Simplifying
-975 + 28x + x2 = 0

Solving
-975 + 28x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '975' to each side of the equation.
-975 + 28x + 975 + x2 = 0 + 975

Reorder the terms:
-975 + 975 + 28x + x2 = 0 + 975

Combine like terms: -975 + 975 = 0
0 + 28x + x2 = 0 + 975
28x + x2 = 0 + 975

Combine like terms: 0 + 975 = 975
28x + x2 = 975

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 975 + 196

Reorder the terms:
196 + 28x + x2 = 975 + 196

Combine like terms: 975 + 196 = 1171
196 + 28x + x2 = 1171

Factor a perfect square on the left side:
(x + 14)(x + 14) = 1171

Calculate the square root of the right side: 34.219877265

Break this problem into two subproblems by setting 
(x + 14) equal to 34.219877265 and -34.219877265.


Subproblem 1
x + 14 = 34.219877265

Simplifying
x + 14 = 34.219877265

Reorder the terms:
14 + x = 34.219877265

Solving
14 + x = 34.219877265

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = 34.219877265 + -14

Combine like terms: 14 + -14 = 0
0 + x = 34.219877265 + -14
x = 34.219877265 + -14

Combine like terms: 34.219877265 + -14 = 20.219877265
x = 20.219877265

Simplifying
x = 20.219877265


Subproblem 2
x + 14 = -34.219877265

Simplifying
x + 14 = -34.219877265

Reorder the terms:
14 + x = -34.219877265

Solving
14 + x = -34.219877265

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = -34.219877265 + -14

Combine like terms: 14 + -14 = 0
0 + x = -34.219877265 + -14
x = -34.219877265 + -14

Combine like terms: -34.219877265 + -14 = -48.219877265
x = -48.219877265

Simplifying
x = -48.219877265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.219877265, -48.219877265}
Solution
x = {20.219877265, -48.219877265}

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