6x^2+45x+25=0

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Solution for 6x^2+45x+25=0 equation: 


Simplifying
6x2 + 45x + 25 = 0

Reorder the terms:
25 + 45x + 6x2 = 0

Solving
25 + 45x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
4.166666667 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-4.166666667' to each side of the equation.
4.166666667 + 7.5x + -4.166666667 + x2 = 0 + -4.166666667

Reorder the terms:
4.166666667 + -4.166666667 + 7.5x + x2 = 0 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + 7.5x + x2 = 0 + -4.166666667
7.5x + x2 = 0 + -4.166666667

Combine like terms: 0 + -4.166666667 = -4.166666667
7.5x + x2 = -4.166666667

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -4.166666667 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -4.166666667 + 14.0625

Combine like terms: -4.166666667 + 14.0625 = 9.895833333
14.0625 + 7.5x + x2 = 9.895833333

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 9.895833333

Calculate the square root of the right side: 3.145764348

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.145764348 and -3.145764348.


Subproblem 1
x + 3.75 = 3.145764348

Simplifying
x + 3.75 = 3.145764348

Reorder the terms:
3.75 + x = 3.145764348

Solving
3.75 + x = 3.145764348

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.145764348 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.145764348 + -3.75
x = 3.145764348 + -3.75

Combine like terms: 3.145764348 + -3.75 = -0.604235652
x = -0.604235652

Simplifying
x = -0.604235652


Subproblem 2
x + 3.75 = -3.145764348

Simplifying
x + 3.75 = -3.145764348

Reorder the terms:
3.75 + x = -3.145764348

Solving
3.75 + x = -3.145764348

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.145764348 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.145764348 + -3.75
x = -3.145764348 + -3.75

Combine like terms: -3.145764348 + -3.75 = -6.895764348
x = -6.895764348

Simplifying
x = -6.895764348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.604235652, -6.895764348}

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