x^2+25x+140.25=0

Solution for x^2+25x+140.25=0 equation:

Simplifying
x2 + 25x + 140.25 = 0

Reorder the terms:
140.25 + 25x + x2 = 0

Solving
140.25 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-140.25' to each side of the equation.
140.25 + 25x + -140.25 + x2 = 0 + -140.25

Reorder the terms:
140.25 + -140.25 + 25x + x2 = 0 + -140.25

Combine like terms: 140.25 + -140.25 = 0.00
0.00 + 25x + x2 = 0 + -140.25
25x + x2 = 0 + -140.25

Combine like terms: 0 + -140.25 = -140.25
25x + x2 = -140.25

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -140.25 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -140.25 + 156.25

Combine like terms: -140.25 + 156.25 = 16
156.25 + 25x + x2 = 16

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + 12.5) equal to 4 and -4.

Subproblem 1
x + 12.5 = 4

Simplifying
x + 12.5 = 4

Reorder the terms:
12.5 + x = 4

Solving
12.5 + x = 4

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 4 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 4 + -12.5
x = 4 + -12.5

Combine like terms: 4 + -12.5 = -8.5
x = -8.5

Simplifying
x = -8.5

Subproblem 2
x + 12.5 = -4

Simplifying
x + 12.5 = -4

Reorder the terms:
12.5 + x = -4

Solving
12.5 + x = -4

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -4 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -4 + -12.5
x = -4 + -12.5

Combine like terms: -4 + -12.5 = -16.5
x = -16.5

Simplifying
x = -16.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.5, -16.5}