3x^2-100x-625=0

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Solution for 3x^2-100x-625=0 equation: 


Simplifying
3x2 + -100x + -625 = 0

Reorder the terms:
-625 + -100x + 3x2 = 0

Solving
-625 + -100x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-208.3333333 + -33.33333333x + x2 = 0

Move the constant term to the right:

Add '208.3333333' to each side of the equation.
-208.3333333 + -33.33333333x + 208.3333333 + x2 = 0 + 208.3333333

Reorder the terms:
-208.3333333 + 208.3333333 + -33.33333333x + x2 = 0 + 208.3333333

Combine like terms: -208.3333333 + 208.3333333 = 0.0000000
0.0000000 + -33.33333333x + x2 = 0 + 208.3333333
-33.33333333x + x2 = 0 + 208.3333333

Combine like terms: 0 + 208.3333333 = 208.3333333
-33.33333333x + x2 = 208.3333333

The x term is -33.33333333x.  Take half its coefficient (-16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
-33.33333333x + 277.7777779 + x2 = 208.3333333 + 277.7777779

Reorder the terms:
277.7777779 + -33.33333333x + x2 = 208.3333333 + 277.7777779

Combine like terms: 208.3333333 + 277.7777779 = 486.1111112
277.7777779 + -33.33333333x + x2 = 486.1111112

Factor a perfect square on the left side:
(x + -16.66666667)(x + -16.66666667) = 486.1111112

Calculate the square root of the right side: 22.047927594

Break this problem into two subproblems by setting 
(x + -16.66666667) equal to 22.047927594 and -22.047927594.


Subproblem 1
x + -16.66666667 = 22.047927594

Simplifying
x + -16.66666667 = 22.047927594

Reorder the terms:
-16.66666667 + x = 22.047927594

Solving
-16.66666667 + x = 22.047927594

Solving for variable 'x'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + x = 22.047927594 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + x = 22.047927594 + 16.66666667
x = 22.047927594 + 16.66666667

Combine like terms: 22.047927594 + 16.66666667 = 38.714594264
x = 38.714594264

Simplifying
x = 38.714594264


Subproblem 2
x + -16.66666667 = -22.047927594

Simplifying
x + -16.66666667 = -22.047927594

Reorder the terms:
-16.66666667 + x = -22.047927594

Solving
-16.66666667 + x = -22.047927594

Solving for variable 'x'.

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

Add '16.66666667' to each side of the equation.
-16.66666667 + 16.66666667 + x = -22.047927594 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + x = -22.047927594 + 16.66666667
x = -22.047927594 + 16.66666667

Combine like terms: -22.047927594 + 16.66666667 = -5.381260924
x = -5.381260924

Simplifying
x = -5.381260924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.714594264, -5.381260924}

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