3x^2+25x=25

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Solution for 3x^2+25x=25 equation: 


Simplifying
3x2 + 25x = 25

Reorder the terms:
25x + 3x2 = 25

Solving
25x + 3x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 25x + 3x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 25x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 8.333333333x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 8.333333333x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 8.333333333x + x2 = 0 + 8.333333333
8.333333333x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
8.333333333x + x2 = 8.333333333

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 8.333333333 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 8.333333333 + 17.36111111

Combine like terms: 8.333333333 + 17.36111111 = 25.694444443
17.36111111 + 8.333333333x + x2 = 25.694444443

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 25.694444443

Calculate the square root of the right side: 5.068968775

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 5.068968775 and -5.068968775.


Subproblem 1
x + 4.166666667 = 5.068968775

Simplifying
x + 4.166666667 = 5.068968775

Reorder the terms:
4.166666667 + x = 5.068968775

Solving
4.166666667 + x = 5.068968775

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 5.068968775 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 5.068968775 + -4.166666667
x = 5.068968775 + -4.166666667

Combine like terms: 5.068968775 + -4.166666667 = 0.902302108
x = 0.902302108

Simplifying
x = 0.902302108


Subproblem 2
x + 4.166666667 = -5.068968775

Simplifying
x + 4.166666667 = -5.068968775

Reorder the terms:
4.166666667 + x = -5.068968775

Solving
4.166666667 + x = -5.068968775

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -5.068968775 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -5.068968775 + -4.166666667
x = -5.068968775 + -4.166666667

Combine like terms: -5.068968775 + -4.166666667 = -9.235635442
x = -9.235635442

Simplifying
x = -9.235635442


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.902302108, -9.235635442}

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