x(x+65)+25=180

Solution for x(x+65)+25=180 equation:

Simplifying
x(x + 65) + 25 = 180

Reorder the terms:
x(65 + x) + 25 = 180
(65 * x + x * x) + 25 = 180
(65x + x2) + 25 = 180

Reorder the terms:
25 + 65x + x2 = 180

Solving
25 + 65x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
25 + -180 + 65x + x2 = 180 + -180

Combine like terms: 25 + -180 = -155
-155 + 65x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-155 + 65x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '155' to each side of the equation.
-155 + 65x + 155 + x2 = 0 + 155

Reorder the terms:
-155 + 155 + 65x + x2 = 0 + 155

Combine like terms: -155 + 155 = 0
0 + 65x + x2 = 0 + 155
65x + x2 = 0 + 155

Combine like terms: 0 + 155 = 155
65x + x2 = 155

The x term is 65x.  Take half its coefficient (32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
65x + 1056.25 + x2 = 155 + 1056.25

Reorder the terms:
1056.25 + 65x + x2 = 155 + 1056.25

Combine like terms: 155 + 1056.25 = 1211.25
1056.25 + 65x + x2 = 1211.25

Factor a perfect square on the left side:
(x + 32.5)(x + 32.5) = 1211.25

Calculate the square root of the right side: 34.803017111

Break this problem into two subproblems by setting 
(x + 32.5) equal to 34.803017111 and -34.803017111.

Subproblem 1
x + 32.5 = 34.803017111

Simplifying
x + 32.5 = 34.803017111

Reorder the terms:
32.5 + x = 34.803017111

Solving
32.5 + x = 34.803017111

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = 34.803017111 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = 34.803017111 + -32.5
x = 34.803017111 + -32.5

Combine like terms: 34.803017111 + -32.5 = 2.303017111
x = 2.303017111

Simplifying
x = 2.303017111

Subproblem 2
x + 32.5 = -34.803017111

Simplifying
x + 32.5 = -34.803017111

Reorder the terms:
32.5 + x = -34.803017111

Solving
32.5 + x = -34.803017111

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = -34.803017111 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = -34.803017111 + -32.5
x = -34.803017111 + -32.5

Combine like terms: -34.803017111 + -32.5 = -67.303017111
x = -67.303017111

Simplifying
x = -67.303017111

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.303017111, -67.303017111}