2x^2+95x+16=0

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Solution for 2x^2+95x+16=0 equation: 


Simplifying
2x2 + 95x + 16 = 0

Reorder the terms:
16 + 95x + 2x2 = 0

Solving
16 + 95x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
8 + 47.5x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 47.5x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 47.5x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 47.5x + x2 = 0 + -8
47.5x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
47.5x + x2 = -8

The x term is 47.5x.  Take half its coefficient (23.75).
Square it (564.0625) and add it to both sides.

Add '564.0625' to each side of the equation.
47.5x + 564.0625 + x2 = -8 + 564.0625

Reorder the terms:
564.0625 + 47.5x + x2 = -8 + 564.0625

Combine like terms: -8 + 564.0625 = 556.0625
564.0625 + 47.5x + x2 = 556.0625

Factor a perfect square on the left side:
(x + 23.75)(x + 23.75) = 556.0625

Calculate the square root of the right side: 23.580977503

Break this problem into two subproblems by setting 
(x + 23.75) equal to 23.580977503 and -23.580977503.


Subproblem 1
x + 23.75 = 23.580977503

Simplifying
x + 23.75 = 23.580977503

Reorder the terms:
23.75 + x = 23.580977503

Solving
23.75 + x = 23.580977503

Solving for variable 'x'.

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

Add '-23.75' to each side of the equation.
23.75 + -23.75 + x = 23.580977503 + -23.75

Combine like terms: 23.75 + -23.75 = 0.00
0.00 + x = 23.580977503 + -23.75
x = 23.580977503 + -23.75

Combine like terms: 23.580977503 + -23.75 = -0.169022497
x = -0.169022497

Simplifying
x = -0.169022497


Subproblem 2
x + 23.75 = -23.580977503

Simplifying
x + 23.75 = -23.580977503

Reorder the terms:
23.75 + x = -23.580977503

Solving
23.75 + x = -23.580977503

Solving for variable 'x'.

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

Add '-23.75' to each side of the equation.
23.75 + -23.75 + x = -23.580977503 + -23.75

Combine like terms: 23.75 + -23.75 = 0.00
0.00 + x = -23.580977503 + -23.75
x = -23.580977503 + -23.75

Combine like terms: -23.580977503 + -23.75 = -47.330977503
x = -47.330977503

Simplifying
x = -47.330977503


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.169022497, -47.330977503}

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