11x^2-14x-28=0

Solution for 11x^2-14x-28=0 equation:

Simplifying
11x2 + -14x + -28 = 0

Reorder the terms:
-28 + -14x + 11x2 = 0

Solving
-28 + -14x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-2.545454545 + -1.272727273x + x2 = 0

Move the constant term to the right:

Add '2.545454545' to each side of the equation.
-2.545454545 + -1.272727273x + 2.545454545 + x2 = 0 + 2.545454545

Reorder the terms:
-2.545454545 + 2.545454545 + -1.272727273x + x2 = 0 + 2.545454545

Combine like terms: -2.545454545 + 2.545454545 = 0.000000000
0.000000000 + -1.272727273x + x2 = 0 + 2.545454545
-1.272727273x + x2 = 0 + 2.545454545

Combine like terms: 0 + 2.545454545 = 2.545454545
-1.272727273x + x2 = 2.545454545

The x term is -1.272727273x.  Take half its coefficient (-0.6363636365).
Square it (0.4049586779) and add it to both sides.

Add '0.4049586779' to each side of the equation.
-1.272727273x + 0.4049586779 + x2 = 2.545454545 + 0.4049586779

Reorder the terms:
0.4049586779 + -1.272727273x + x2 = 2.545454545 + 0.4049586779

Combine like terms: 2.545454545 + 0.4049586779 = 2.9504132229
0.4049586779 + -1.272727273x + x2 = 2.9504132229

Factor a perfect square on the left side:
(x + -0.6363636365)(x + -0.6363636365) = 2.9504132229

Calculate the square root of the right side: 1.717676693

Break this problem into two subproblems by setting 
(x + -0.6363636365) equal to 1.717676693 and -1.717676693.

Subproblem 1
x + -0.6363636365 = 1.717676693

Simplifying
x + -0.6363636365 = 1.717676693

Reorder the terms:
-0.6363636365 + x = 1.717676693

Solving
-0.6363636365 + x = 1.717676693

Solving for variable 'x'.

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

Add '0.6363636365' to each side of the equation.
-0.6363636365 + 0.6363636365 + x = 1.717676693 + 0.6363636365

Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000
0.0000000000 + x = 1.717676693 + 0.6363636365
x = 1.717676693 + 0.6363636365

Combine like terms: 1.717676693 + 0.6363636365 = 2.3540403295
x = 2.3540403295

Simplifying
x = 2.3540403295

Subproblem 2
x + -0.6363636365 = -1.717676693

Simplifying
x + -0.6363636365 = -1.717676693

Reorder the terms:
-0.6363636365 + x = -1.717676693

Solving
-0.6363636365 + x = -1.717676693

Solving for variable 'x'.

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

Add '0.6363636365' to each side of the equation.
-0.6363636365 + 0.6363636365 + x = -1.717676693 + 0.6363636365

Combine like terms: -0.6363636365 + 0.6363636365 = 0.0000000000
0.0000000000 + x = -1.717676693 + 0.6363636365
x = -1.717676693 + 0.6363636365

Combine like terms: -1.717676693 + 0.6363636365 = -1.0813130565
x = -1.0813130565

Simplifying
x = -1.0813130565

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3540403295, -1.0813130565}