26-(4x-11)=-5x(x+7)

Solution for 26-(4x-11)=-5x(x+7) equation:

Simplifying
26 + -1(4x + -11) = -5x(x + 7)

Reorder the terms:
26 + -1(-11 + 4x) = -5x(x + 7)
26 + (-11 * -1 + 4x * -1) = -5x(x + 7)
26 + (11 + -4x) = -5x(x + 7)

Combine like terms: 26 + 11 = 37
37 + -4x = -5x(x + 7)

Reorder the terms:
37 + -4x = -5x(7 + x)
37 + -4x = (7 * -5x + x * -5x)
37 + -4x = (-35x + -5x2)

Solving
37 + -4x = -35x + -5x2

Solving for variable 'x'.

Combine like terms: -4x + 35x = 31x
37 + 31x + 5x2 = -35x + -5x2 + 35x + 5x2

Reorder the terms:
37 + 31x + 5x2 = -35x + 35x + -5x2 + 5x2

Combine like terms: -35x + 35x = 0
37 + 31x + 5x2 = 0 + -5x2 + 5x2
37 + 31x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
37 + 31x + 5x2 = 0

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

Divide each side by '5'.
7.4 + 6.2x + x2 = 0

Move the constant term to the right:

Add '-7.4' to each side of the equation.
7.4 + 6.2x + -7.4 + x2 = 0 + -7.4

Reorder the terms:
7.4 + -7.4 + 6.2x + x2 = 0 + -7.4

Combine like terms: 7.4 + -7.4 = 0.0
0.0 + 6.2x + x2 = 0 + -7.4
6.2x + x2 = 0 + -7.4

Combine like terms: 0 + -7.4 = -7.4
6.2x + x2 = -7.4

The x term is 6.2x.  Take half its coefficient (3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
6.2x + 9.61 + x2 = -7.4 + 9.61

Reorder the terms:
9.61 + 6.2x + x2 = -7.4 + 9.61

Combine like terms: -7.4 + 9.61 = 2.21
9.61 + 6.2x + x2 = 2.21

Factor a perfect square on the left side:
(x + 3.1)(x + 3.1) = 2.21

Calculate the square root of the right side: 1.486606875

Break this problem into two subproblems by setting 
(x + 3.1) equal to 1.486606875 and -1.486606875.

Subproblem 1
x + 3.1 = 1.486606875

Simplifying
x + 3.1 = 1.486606875

Reorder the terms:
3.1 + x = 1.486606875

Solving
3.1 + x = 1.486606875

Solving for variable 'x'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + x = 1.486606875 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + x = 1.486606875 + -3.1
x = 1.486606875 + -3.1

Combine like terms: 1.486606875 + -3.1 = -1.613393125
x = -1.613393125

Simplifying
x = -1.613393125

Subproblem 2
x + 3.1 = -1.486606875

Simplifying
x + 3.1 = -1.486606875

Reorder the terms:
3.1 + x = -1.486606875

Solving
3.1 + x = -1.486606875

Solving for variable 'x'.

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

Add '-3.1' to each side of the equation.
3.1 + -3.1 + x = -1.486606875 + -3.1

Combine like terms: 3.1 + -3.1 = 0.0
0.0 + x = -1.486606875 + -3.1
x = -1.486606875 + -3.1

Combine like terms: -1.486606875 + -3.1 = -4.586606875
x = -4.586606875

Simplifying
x = -4.586606875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.613393125, -4.586606875}