x^2+5x-37.5=0

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Solution for x^2+5x-37.5=0 equation: 


Simplifying
x2 + 5x + -37.5 = 0

Reorder the terms:
-37.5 + 5x + x2 = 0

Solving
-37.5 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '37.5' to each side of the equation.
-37.5 + 5x + 37.5 + x2 = 0 + 37.5

Reorder the terms:
-37.5 + 37.5 + 5x + x2 = 0 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + 5x + x2 = 0 + 37.5
5x + x2 = 0 + 37.5

Combine like terms: 0 + 37.5 = 37.5
5x + x2 = 37.5

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 = 37.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 37.5 + 6.25

Combine like terms: 37.5 + 6.25 = 43.75
6.25 + 5x + x2 = 43.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 43.75

Calculate the square root of the right side: 6.614378278

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.614378278 and -6.614378278.


Subproblem 1
x + 2.5 = 6.614378278

Simplifying
x + 2.5 = 6.614378278

Reorder the terms:
2.5 + x = 6.614378278

Solving
2.5 + x = 6.614378278

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 = 6.614378278 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.614378278 + -2.5
x = 6.614378278 + -2.5

Combine like terms: 6.614378278 + -2.5 = 4.114378278
x = 4.114378278

Simplifying
x = 4.114378278


Subproblem 2
x + 2.5 = -6.614378278

Simplifying
x + 2.5 = -6.614378278

Reorder the terms:
2.5 + x = -6.614378278

Solving
2.5 + x = -6.614378278

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 = -6.614378278 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.614378278 + -2.5
x = -6.614378278 + -2.5

Combine like terms: -6.614378278 + -2.5 = -9.114378278
x = -9.114378278

Simplifying
x = -9.114378278


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.114378278, -9.114378278}

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