x^2-700x+11180=0

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Solution for x^2-700x+11180=0 equation: 


Simplifying
x2 + -700x + 11180 = 0

Reorder the terms:
11180 + -700x + x2 = 0

Solving
11180 + -700x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11180' to each side of the equation.
11180 + -700x + -11180 + x2 = 0 + -11180

Reorder the terms:
11180 + -11180 + -700x + x2 = 0 + -11180

Combine like terms: 11180 + -11180 = 0
0 + -700x + x2 = 0 + -11180
-700x + x2 = 0 + -11180

Combine like terms: 0 + -11180 = -11180
-700x + x2 = -11180

The x term is -700x.  Take half its coefficient (-350).
Square it (122500) and add it to both sides.

Add '122500' to each side of the equation.
-700x + 122500 + x2 = -11180 + 122500

Reorder the terms:
122500 + -700x + x2 = -11180 + 122500

Combine like terms: -11180 + 122500 = 111320
122500 + -700x + x2 = 111320

Factor a perfect square on the left side:
(x + -350)(x + -350) = 111320

Calculate the square root of the right side: 333.646519538

Break this problem into two subproblems by setting 
(x + -350) equal to 333.646519538 and -333.646519538.


Subproblem 1
x + -350 = 333.646519538

Simplifying
x + -350 = 333.646519538

Reorder the terms:
-350 + x = 333.646519538

Solving
-350 + x = 333.646519538

Solving for variable 'x'.

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

Add '350' to each side of the equation.
-350 + 350 + x = 333.646519538 + 350

Combine like terms: -350 + 350 = 0
0 + x = 333.646519538 + 350
x = 333.646519538 + 350

Combine like terms: 333.646519538 + 350 = 683.646519538
x = 683.646519538

Simplifying
x = 683.646519538


Subproblem 2
x + -350 = -333.646519538

Simplifying
x + -350 = -333.646519538

Reorder the terms:
-350 + x = -333.646519538

Solving
-350 + x = -333.646519538

Solving for variable 'x'.

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

Add '350' to each side of the equation.
-350 + 350 + x = -333.646519538 + 350

Combine like terms: -350 + 350 = 0
0 + x = -333.646519538 + 350
x = -333.646519538 + 350

Combine like terms: -333.646519538 + 350 = 16.353480462
x = 16.353480462

Simplifying
x = 16.353480462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {683.646519538, 16.353480462}

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