x^2+11x-1569.75=0

Solution for x^2+11x-1569.75=0 equation:

Simplifying
x2 + 11x + -1569.75 = 0

Reorder the terms:
-1569.75 + 11x + x2 = 0

Solving
-1569.75 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1569.75' to each side of the equation.
-1569.75 + 11x + 1569.75 + x2 = 0 + 1569.75

Reorder the terms:
-1569.75 + 1569.75 + 11x + x2 = 0 + 1569.75

Combine like terms: -1569.75 + 1569.75 = 0.00
0.00 + 11x + x2 = 0 + 1569.75
11x + x2 = 0 + 1569.75

Combine like terms: 0 + 1569.75 = 1569.75
11x + x2 = 1569.75

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 1569.75 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 1569.75 + 30.25

Combine like terms: 1569.75 + 30.25 = 1600
30.25 + 11x + x2 = 1600

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 1600

Calculate the square root of the right side: 40

Break this problem into two subproblems by setting 
(x + 5.5) equal to 40 and -40.

Subproblem 1
x + 5.5 = 40

Simplifying
x + 5.5 = 40

Reorder the terms:
5.5 + x = 40

Solving
5.5 + x = 40

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 40 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 40 + -5.5
x = 40 + -5.5

Combine like terms: 40 + -5.5 = 34.5
x = 34.5

Simplifying
x = 34.5

Subproblem 2
x + 5.5 = -40

Simplifying
x + 5.5 = -40

Reorder the terms:
5.5 + x = -40

Solving
5.5 + x = -40

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -40 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -40 + -5.5
x = -40 + -5.5

Combine like terms: -40 + -5.5 = -45.5
x = -45.5

Simplifying
x = -45.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.5, -45.5}