x^2+5x-18.75=0

Solution for x^2+5x-18.75=0 equation:

Simplifying
x2 + 5x + -18.75 = 0

Reorder the terms:
-18.75 + 5x + x2 = 0

Solving
-18.75 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + 5x + 18.75 + x2 = 0 + 18.75

Reorder the terms:
-18.75 + 18.75 + 5x + x2 = 0 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + 5x + x2 = 0 + 18.75
5x + x2 = 0 + 18.75

Combine like terms: 0 + 18.75 = 18.75
5x + x2 = 18.75

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 = 18.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 18.75 + 6.25

Combine like terms: 18.75 + 6.25 = 25
6.25 + 5x + x2 = 25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5 and -5.

Subproblem 1
x + 2.5 = 5

Simplifying
x + 2.5 = 5

Reorder the terms:
2.5 + x = 5

Solving
2.5 + x = 5

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 = 5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5 + -2.5
x = 5 + -2.5

Combine like terms: 5 + -2.5 = 2.5
x = 2.5

Simplifying
x = 2.5

Subproblem 2
x + 2.5 = -5

Simplifying
x + 2.5 = -5

Reorder the terms:
2.5 + x = -5

Solving
2.5 + x = -5

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 = -5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5 + -2.5
x = -5 + -2.5

Combine like terms: -5 + -2.5 = -7.5
x = -7.5

Simplifying
x = -7.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5, -7.5}