2x^2-4x-51=0

Solution for 2x^2-4x-51=0 equation:

Simplifying
2x2 + -4x + -51 = 0

Reorder the terms:
-51 + -4x + 2x2 = 0

Solving
-51 + -4x + 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'.
-25.5 + -2x + x2 = 0

Move the constant term to the right:

Add '25.5' to each side of the equation.
-25.5 + -2x + 25.5 + x2 = 0 + 25.5

Reorder the terms:
-25.5 + 25.5 + -2x + x2 = 0 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + -2x + x2 = 0 + 25.5
-2x + x2 = 0 + 25.5

Combine like terms: 0 + 25.5 = 25.5
-2x + x2 = 25.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 25.5 + 1

Reorder the terms:
1 + -2x + x2 = 25.5 + 1

Combine like terms: 25.5 + 1 = 26.5
1 + -2x + x2 = 26.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 26.5

Calculate the square root of the right side: 5.14781507

Break this problem into two subproblems by setting 
(x + -1) equal to 5.14781507 and -5.14781507.

Subproblem 1
x + -1 = 5.14781507

Simplifying
x + -1 = 5.14781507

Reorder the terms:
-1 + x = 5.14781507

Solving
-1 + x = 5.14781507

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 5.14781507 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.14781507 + 1
x = 5.14781507 + 1

Combine like terms: 5.14781507 + 1 = 6.14781507
x = 6.14781507

Simplifying
x = 6.14781507

Subproblem 2
x + -1 = -5.14781507

Simplifying
x + -1 = -5.14781507

Reorder the terms:
-1 + x = -5.14781507

Solving
-1 + x = -5.14781507

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -5.14781507 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.14781507 + 1
x = -5.14781507 + 1

Combine like terms: -5.14781507 + 1 = -4.14781507
x = -4.14781507

Simplifying
x = -4.14781507

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.14781507, -4.14781507}