x^2+75x=5625

Solution for x^2+75x=5625 equation:

Simplifying
x2 + 75x = 5625

Reorder the terms:
75x + x2 = 5625

Solving
75x + x2 = 5625

Solving for variable 'x'.

Reorder the terms:
-5625 + 75x + x2 = 5625 + -5625

Combine like terms: 5625 + -5625 = 0
-5625 + 75x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5625' to each side of the equation.
-5625 + 75x + 5625 + x2 = 0 + 5625

Reorder the terms:
-5625 + 5625 + 75x + x2 = 0 + 5625

Combine like terms: -5625 + 5625 = 0
0 + 75x + x2 = 0 + 5625
75x + x2 = 0 + 5625

Combine like terms: 0 + 5625 = 5625
75x + x2 = 5625

The x term is 75x.  Take half its coefficient (37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
75x + 1406.25 + x2 = 5625 + 1406.25

Reorder the terms:
1406.25 + 75x + x2 = 5625 + 1406.25

Combine like terms: 5625 + 1406.25 = 7031.25
1406.25 + 75x + x2 = 7031.25

Factor a perfect square on the left side:
(x + 37.5)(x + 37.5) = 7031.25

Calculate the square root of the right side: 83.852549156

Break this problem into two subproblems by setting 
(x + 37.5) equal to 83.852549156 and -83.852549156.

Subproblem 1
x + 37.5 = 83.852549156

Simplifying
x + 37.5 = 83.852549156

Reorder the terms:
37.5 + x = 83.852549156

Solving
37.5 + x = 83.852549156

Solving for variable 'x'.

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

Add '-37.5' to each side of the equation.
37.5 + -37.5 + x = 83.852549156 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + x = 83.852549156 + -37.5
x = 83.852549156 + -37.5

Combine like terms: 83.852549156 + -37.5 = 46.352549156
x = 46.352549156

Simplifying
x = 46.352549156

Subproblem 2
x + 37.5 = -83.852549156

Simplifying
x + 37.5 = -83.852549156

Reorder the terms:
37.5 + x = -83.852549156

Solving
37.5 + x = -83.852549156

Solving for variable 'x'.

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

Add '-37.5' to each side of the equation.
37.5 + -37.5 + x = -83.852549156 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + x = -83.852549156 + -37.5
x = -83.852549156 + -37.5

Combine like terms: -83.852549156 + -37.5 = -121.352549156
x = -121.352549156

Simplifying
x = -121.352549156

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.352549156, -121.352549156}