8x^2+36x+25=0

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Solution for 8x^2+36x+25=0 equation: 


Simplifying
8x2 + 36x + 25 = 0

Reorder the terms:
25 + 36x + 8x2 = 0

Solving
25 + 36x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
3.125 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + 4.5x + -3.125 + x2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + 4.5x + x2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + 4.5x + x2 = 0 + -3.125
4.5x + x2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
4.5x + x2 = -3.125

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -3.125 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -3.125 + 5.0625

Combine like terms: -3.125 + 5.0625 = 1.9375
5.0625 + 4.5x + x2 = 1.9375

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 1.9375

Calculate the square root of the right side: 1.391941091

Break this problem into two subproblems by setting 
(x + 2.25) equal to 1.391941091 and -1.391941091.


Subproblem 1
x + 2.25 = 1.391941091

Simplifying
x + 2.25 = 1.391941091

Reorder the terms:
2.25 + x = 1.391941091

Solving
2.25 + x = 1.391941091

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 1.391941091 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 1.391941091 + -2.25
x = 1.391941091 + -2.25

Combine like terms: 1.391941091 + -2.25 = -0.858058909
x = -0.858058909

Simplifying
x = -0.858058909


Subproblem 2
x + 2.25 = -1.391941091

Simplifying
x + 2.25 = -1.391941091

Reorder the terms:
2.25 + x = -1.391941091

Solving
2.25 + x = -1.391941091

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -1.391941091 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -1.391941091 + -2.25
x = -1.391941091 + -2.25

Combine like terms: -1.391941091 + -2.25 = -3.641941091
x = -3.641941091

Simplifying
x = -3.641941091


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.858058909, -3.641941091}

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