(x+5)2+(x-2)2+(x-7)(x+7)=11x+30

Solution for (x+5)2+(x-2)2+(x-7)(x+7)=11x+30 equation:

Simplifying
(x + 5) * 2 + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30

Reorder the terms:
(5 + x) * 2 + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30

Reorder the terms for easier multiplication:
2(5 + x) + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30
(5 * 2 + x * 2) + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30
(10 + 2x) + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30

Reorder the terms:
10 + 2x + (-2 + x) * 2 + (x + -7)(x + 7) = 11x + 30

Reorder the terms for easier multiplication:
10 + 2x + 2(-2 + x) + (x + -7)(x + 7) = 11x + 30
10 + 2x + (-2 * 2 + x * 2) + (x + -7)(x + 7) = 11x + 30
10 + 2x + (-4 + 2x) + (x + -7)(x + 7) = 11x + 30

Reorder the terms:
10 + 2x + -4 + 2x + (-7 + x)(x + 7) = 11x + 30

Reorder the terms:
10 + 2x + -4 + 2x + (-7 + x)(7 + x) = 11x + 30

Multiply (-7 + x) * (7 + x)
10 + 2x + -4 + 2x + (-7(7 + x) + x(7 + x)) = 11x + 30
10 + 2x + -4 + 2x + ((7 * -7 + x * -7) + x(7 + x)) = 11x + 30
10 + 2x + -4 + 2x + ((-49 + -7x) + x(7 + x)) = 11x + 30
10 + 2x + -4 + 2x + (-49 + -7x + (7 * x + x * x)) = 11x + 30
10 + 2x + -4 + 2x + (-49 + -7x + (7x + x2)) = 11x + 30

Combine like terms: -7x + 7x = 0
10 + 2x + -4 + 2x + (-49 + 0 + x2) = 11x + 30
10 + 2x + -4 + 2x + (-49 + x2) = 11x + 30

Reorder the terms:
10 + -4 + -49 + 2x + 2x + x2 = 11x + 30

Combine like terms: 10 + -4 = 6
6 + -49 + 2x + 2x + x2 = 11x + 30

Combine like terms: 6 + -49 = -43
-43 + 2x + 2x + x2 = 11x + 30

Combine like terms: 2x + 2x = 4x
-43 + 4x + x2 = 11x + 30

Reorder the terms:
-43 + 4x + x2 = 30 + 11x

Solving
-43 + 4x + x2 = 30 + 11x

Solving for variable 'x'.

Reorder the terms:
-43 + -30 + 4x + -11x + x2 = 30 + 11x + -30 + -11x

Combine like terms: -43 + -30 = -73
-73 + 4x + -11x + x2 = 30 + 11x + -30 + -11x

Combine like terms: 4x + -11x = -7x
-73 + -7x + x2 = 30 + 11x + -30 + -11x

Reorder the terms:
-73 + -7x + x2 = 30 + -30 + 11x + -11x

Combine like terms: 30 + -30 = 0
-73 + -7x + x2 = 0 + 11x + -11x
-73 + -7x + x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-73 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + -7x + 73 + x2 = 0 + 73

Reorder the terms:
-73 + 73 + -7x + x2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + -7x + x2 = 0 + 73
-7x + x2 = 0 + 73

Combine like terms: 0 + 73 = 73
-7x + x2 = 73

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 73 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 73 + 12.25

Combine like terms: 73 + 12.25 = 85.25
12.25 + -7x + x2 = 85.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + -3.5) equal to 9.233092656 and -9.233092656.

Subproblem 1
x + -3.5 = 9.233092656

Simplifying
x + -3.5 = 9.233092656

Reorder the terms:
-3.5 + x = 9.233092656

Solving
-3.5 + x = 9.233092656

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 9.233092656 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 9.233092656 + 3.5
x = 9.233092656 + 3.5

Combine like terms: 9.233092656 + 3.5 = 12.733092656
x = 12.733092656

Simplifying
x = 12.733092656

Subproblem 2
x + -3.5 = -9.233092656

Simplifying
x + -3.5 = -9.233092656

Reorder the terms:
-3.5 + x = -9.233092656

Solving
-3.5 + x = -9.233092656

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -9.233092656 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -9.233092656 + 3.5
x = -9.233092656 + 3.5

Combine like terms: -9.233092656 + 3.5 = -5.733092656
x = -5.733092656

Simplifying
x = -5.733092656

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.733092656, -5.733092656}