X^2+630X+61875=0

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Solution for X^2+630X+61875=0 equation: 


Simplifying
X2 + 630X + 61875 = 0

Reorder the terms:
61875 + 630X + X2 = 0

Solving
61875 + 630X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-61875' to each side of the equation.
61875 + 630X + -61875 + X2 = 0 + -61875

Reorder the terms:
61875 + -61875 + 630X + X2 = 0 + -61875

Combine like terms: 61875 + -61875 = 0
0 + 630X + X2 = 0 + -61875
630X + X2 = 0 + -61875

Combine like terms: 0 + -61875 = -61875
630X + X2 = -61875

The X term is 630X.  Take half its coefficient (315).
Square it (99225) and add it to both sides.

Add '99225' to each side of the equation.
630X + 99225 + X2 = -61875 + 99225

Reorder the terms:
99225 + 630X + X2 = -61875 + 99225

Combine like terms: -61875 + 99225 = 37350
99225 + 630X + X2 = 37350

Factor a perfect square on the left side:
(X + 315)(X + 315) = 37350

Calculate the square root of the right side: 193.261480901

Break this problem into two subproblems by setting 
(X + 315) equal to 193.261480901 and -193.261480901.


Subproblem 1
X + 315 = 193.261480901

Simplifying
X + 315 = 193.261480901

Reorder the terms:
315 + X = 193.261480901

Solving
315 + X = 193.261480901

Solving for variable 'X'.

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

Add '-315' to each side of the equation.
315 + -315 + X = 193.261480901 + -315

Combine like terms: 315 + -315 = 0
0 + X = 193.261480901 + -315
X = 193.261480901 + -315

Combine like terms: 193.261480901 + -315 = -121.738519099
X = -121.738519099

Simplifying
X = -121.738519099


Subproblem 2
X + 315 = -193.261480901

Simplifying
X + 315 = -193.261480901

Reorder the terms:
315 + X = -193.261480901

Solving
315 + X = -193.261480901

Solving for variable 'X'.

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

Add '-315' to each side of the equation.
315 + -315 + X = -193.261480901 + -315

Combine like terms: 315 + -315 = 0
0 + X = -193.261480901 + -315
X = -193.261480901 + -315

Combine like terms: -193.261480901 + -315 = -508.261480901
X = -508.261480901

Simplifying
X = -508.261480901


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-121.738519099, -508.261480901}

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