1.25x^2+7x+5=0

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Solution for 1.25x^2+7x+5=0 equation: 


Simplifying
1.25x2 + 7x + 5 = 0

Reorder the terms:
5 + 7x + 1.25x2 = 0

Solving
5 + 7x + 1.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
1.25 the coefficient of the squared term: 

Divide each side by '1.25'.
4 + 5.6x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 5.6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 5.6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5.6x + x2 = 0 + -4
5.6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
5.6x + x2 = -4

The x term is 5.6x.  Take half its coefficient (2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
5.6x + 7.84 + x2 = -4 + 7.84

Reorder the terms:
7.84 + 5.6x + x2 = -4 + 7.84

Combine like terms: -4 + 7.84 = 3.84
7.84 + 5.6x + x2 = 3.84

Factor a perfect square on the left side:
(x + 2.8)(x + 2.8) = 3.84

Calculate the square root of the right side: 1.959591794

Break this problem into two subproblems by setting 
(x + 2.8) equal to 1.959591794 and -1.959591794.


Subproblem 1
x + 2.8 = 1.959591794

Simplifying
x + 2.8 = 1.959591794

Reorder the terms:
2.8 + x = 1.959591794

Solving
2.8 + x = 1.959591794

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = 1.959591794 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = 1.959591794 + -2.8
x = 1.959591794 + -2.8

Combine like terms: 1.959591794 + -2.8 = -0.840408206
x = -0.840408206

Simplifying
x = -0.840408206


Subproblem 2
x + 2.8 = -1.959591794

Simplifying
x + 2.8 = -1.959591794

Reorder the terms:
2.8 + x = -1.959591794

Solving
2.8 + x = -1.959591794

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = -1.959591794 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = -1.959591794 + -2.8
x = -1.959591794 + -2.8

Combine like terms: -1.959591794 + -2.8 = -4.759591794
x = -4.759591794

Simplifying
x = -4.759591794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.840408206, -4.759591794}

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