x^2+11x+20x=10x+76

Solution for x^2+11x+20x=10x+76 equation:

Simplifying
x2 + 11x + 20x = 10x + 76

Reorder the terms:
11x + 20x + x2 = 10x + 76

Combine like terms: 11x + 20x = 31x
31x + x2 = 10x + 76

Reorder the terms:
31x + x2 = 76 + 10x

Solving
31x + x2 = 76 + 10x

Solving for variable 'x'.

Reorder the terms:
-76 + 31x + -10x + x2 = 76 + 10x + -76 + -10x

Combine like terms: 31x + -10x = 21x
-76 + 21x + x2 = 76 + 10x + -76 + -10x

Reorder the terms:
-76 + 21x + x2 = 76 + -76 + 10x + -10x

Combine like terms: 76 + -76 = 0
-76 + 21x + x2 = 0 + 10x + -10x
-76 + 21x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-76 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + 21x + 76 + x2 = 0 + 76

Reorder the terms:
-76 + 76 + 21x + x2 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + 21x + x2 = 0 + 76
21x + x2 = 0 + 76

Combine like terms: 0 + 76 = 76
21x + x2 = 76

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 76 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 76 + 110.25

Combine like terms: 76 + 110.25 = 186.25
110.25 + 21x + x2 = 186.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 186.25

Calculate the square root of the right side: 13.647344064

Break this problem into two subproblems by setting 
(x + 10.5) equal to 13.647344064 and -13.647344064.

Subproblem 1
x + 10.5 = 13.647344064

Simplifying
x + 10.5 = 13.647344064

Reorder the terms:
10.5 + x = 13.647344064

Solving
10.5 + x = 13.647344064

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 13.647344064 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 13.647344064 + -10.5
x = 13.647344064 + -10.5

Combine like terms: 13.647344064 + -10.5 = 3.147344064
x = 3.147344064

Simplifying
x = 3.147344064

Subproblem 2
x + 10.5 = -13.647344064

Simplifying
x + 10.5 = -13.647344064

Reorder the terms:
10.5 + x = -13.647344064

Solving
10.5 + x = -13.647344064

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -13.647344064 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -13.647344064 + -10.5
x = -13.647344064 + -10.5

Combine like terms: -13.647344064 + -10.5 = -24.147344064
x = -24.147344064

Simplifying
x = -24.147344064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.147344064, -24.147344064}