x^2+5x-7.5=0

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Solution for x^2+5x-7.5=0 equation: 


Simplifying
x2 + 5x + -7.5 = 0

Reorder the terms:
-7.5 + 5x + x2 = 0

Solving
-7.5 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 5x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 5x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 5x + x2 = 0 + 7.5
5x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
5x + x2 = 7.5

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 = 7.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 7.5 + 6.25

Combine like terms: 7.5 + 6.25 = 13.75
6.25 + 5x + x2 = 13.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.708099244 and -3.708099244.


Subproblem 1
x + 2.5 = 3.708099244

Simplifying
x + 2.5 = 3.708099244

Reorder the terms:
2.5 + x = 3.708099244

Solving
2.5 + x = 3.708099244

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 = 3.708099244 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.708099244 + -2.5
x = 3.708099244 + -2.5

Combine like terms: 3.708099244 + -2.5 = 1.208099244
x = 1.208099244

Simplifying
x = 1.208099244


Subproblem 2
x + 2.5 = -3.708099244

Simplifying
x + 2.5 = -3.708099244

Reorder the terms:
2.5 + x = -3.708099244

Solving
2.5 + x = -3.708099244

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 = -3.708099244 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.708099244 + -2.5
x = -3.708099244 + -2.5

Combine like terms: -3.708099244 + -2.5 = -6.208099244
x = -6.208099244

Simplifying
x = -6.208099244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.208099244, -6.208099244}

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