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 = 508.261480901
x = 508.261480901

Simplifying
x = 508.261480901


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 = 121.738519099
x = 121.738519099

Simplifying
x = 121.738519099


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

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