7x(x+5)+2=37

Solution for 7x(x+5)+2=37 equation:

Simplifying
7x(x + 5) + 2 = 37

Reorder the terms:
7x(5 + x) + 2 = 37
(5 * 7x + x * 7x) + 2 = 37
(35x + 7x2) + 2 = 37

Reorder the terms:
2 + 35x + 7x2 = 37

Solving
2 + 35x + 7x2 = 37

Solving for variable 'x'.

Reorder the terms:
2 + -37 + 35x + 7x2 = 37 + -37

Combine like terms: 2 + -37 = -35
-35 + 35x + 7x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-35 + 35x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + 5x + x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-5 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 5x + x2 = 0

Solving
-5 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 5x + x2 = 0 + 5

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

Combine like terms: 0 + 5 = 5
5x + x2 = 5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5x + x2 = 11.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.354101966 and -3.354101966.

Subproblem 1
x + 2.5 = 3.354101966

Simplifying
x + 2.5 = 3.354101966

Reorder the terms:
2.5 + x = 3.354101966

Solving
2.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.354101966 + -2.5
x = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
x = 0.854101966

Simplifying
x = 0.854101966

Subproblem 2
x + 2.5 = -3.354101966

Simplifying
x + 2.5 = -3.354101966

Reorder the terms:
2.5 + x = -3.354101966

Solving
2.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.354101966 + -2.5
x = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
x = -5.854101966

Simplifying
x = -5.854101966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.854101966, -5.854101966}
Solution
x = {0.854101966, -5.854101966}