2x^2+51x+34=0

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Solution for 2x^2+51x+34=0 equation: 


Simplifying
2x2 + 51x + 34 = 0

Reorder the terms:
34 + 51x + 2x2 = 0

Solving
34 + 51x + 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'.
17 + 25.5x + x2 = 0

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 25.5x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 25.5x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 25.5x + x2 = 0 + -17
25.5x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
25.5x + x2 = -17

The x term is 25.5x.  Take half its coefficient (12.75).
Square it (162.5625) and add it to both sides.

Add '162.5625' to each side of the equation.
25.5x + 162.5625 + x2 = -17 + 162.5625

Reorder the terms:
162.5625 + 25.5x + x2 = -17 + 162.5625

Combine like terms: -17 + 162.5625 = 145.5625
162.5625 + 25.5x + x2 = 145.5625

Factor a perfect square on the left side:
(x + 12.75)(x + 12.75) = 145.5625

Calculate the square root of the right side: 12.064928512

Break this problem into two subproblems by setting 
(x + 12.75) equal to 12.064928512 and -12.064928512.


Subproblem 1
x + 12.75 = 12.064928512

Simplifying
x + 12.75 = 12.064928512

Reorder the terms:
12.75 + x = 12.064928512

Solving
12.75 + x = 12.064928512

Solving for variable 'x'.

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

Add '-12.75' to each side of the equation.
12.75 + -12.75 + x = 12.064928512 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + x = 12.064928512 + -12.75
x = 12.064928512 + -12.75

Combine like terms: 12.064928512 + -12.75 = -0.685071488
x = -0.685071488

Simplifying
x = -0.685071488


Subproblem 2
x + 12.75 = -12.064928512

Simplifying
x + 12.75 = -12.064928512

Reorder the terms:
12.75 + x = -12.064928512

Solving
12.75 + x = -12.064928512

Solving for variable 'x'.

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

Add '-12.75' to each side of the equation.
12.75 + -12.75 + x = -12.064928512 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + x = -12.064928512 + -12.75
x = -12.064928512 + -12.75

Combine like terms: -12.064928512 + -12.75 = -24.814928512
x = -24.814928512

Simplifying
x = -24.814928512


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.685071488, -24.814928512}

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