5x^2+25x+7=0

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Solution for 5x^2+25x+7=0 equation: 


Simplifying
5x2 + 25x + 7 = 0

Reorder the terms:
7 + 25x + 5x2 = 0

Solving
7 + 25x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.4 + 5x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 5x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 5x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 5x + x2 = 0 + -1.4
5x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
5x + x2 = -1.4

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 = -1.4 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1.4 + 6.25

Combine like terms: -1.4 + 6.25 = 4.85
6.25 + 5x + x2 = 4.85

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 4.85

Calculate the square root of the right side: 2.202271555

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.202271555 and -2.202271555.


Subproblem 1
x + 2.5 = 2.202271555

Simplifying
x + 2.5 = 2.202271555

Reorder the terms:
2.5 + x = 2.202271555

Solving
2.5 + x = 2.202271555

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 = 2.202271555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.202271555 + -2.5
x = 2.202271555 + -2.5

Combine like terms: 2.202271555 + -2.5 = -0.297728445
x = -0.297728445

Simplifying
x = -0.297728445


Subproblem 2
x + 2.5 = -2.202271555

Simplifying
x + 2.5 = -2.202271555

Reorder the terms:
2.5 + x = -2.202271555

Solving
2.5 + x = -2.202271555

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 = -2.202271555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.202271555 + -2.5
x = -2.202271555 + -2.5

Combine like terms: -2.202271555 + -2.5 = -4.702271555
x = -4.702271555

Simplifying
x = -4.702271555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.297728445, -4.702271555}

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