5x^2+25x+4=0

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Solution for 5x^2+25x+4=0 equation: 


Simplifying
5x2 + 25x + 4 = 0

Reorder the terms:
4 + 25x + 5x2 = 0

Solving
4 + 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'.
0.8 + 5x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + 5x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + 5x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + 5x + x2 = 0 + -0.8
5x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
5x + x2 = -0.8

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 = -0.8 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -0.8 + 6.25

Combine like terms: -0.8 + 6.25 = 5.45
6.25 + 5x + x2 = 5.45

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5.45

Calculate the square root of the right side: 2.334523506

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.334523506 and -2.334523506.


Subproblem 1
x + 2.5 = 2.334523506

Simplifying
x + 2.5 = 2.334523506

Reorder the terms:
2.5 + x = 2.334523506

Solving
2.5 + x = 2.334523506

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 = 2.334523506 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.334523506 + -2.5
x = 2.334523506 + -2.5

Combine like terms: 2.334523506 + -2.5 = -0.165476494
x = -0.165476494

Simplifying
x = -0.165476494


Subproblem 2
x + 2.5 = -2.334523506

Simplifying
x + 2.5 = -2.334523506

Reorder the terms:
2.5 + x = -2.334523506

Solving
2.5 + x = -2.334523506

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 = -2.334523506 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.334523506 + -2.5
x = -2.334523506 + -2.5

Combine like terms: -2.334523506 + -2.5 = -4.834523506
x = -4.834523506

Simplifying
x = -4.834523506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.165476494, -4.834523506}

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