x^2-35x-555=0

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Solution for x^2-35x-555=0 equation: 


Simplifying
x2 + -35x + -555 = 0

Reorder the terms:
-555 + -35x + x2 = 0

Solving
-555 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '555' to each side of the equation.
-555 + -35x + 555 + x2 = 0 + 555

Reorder the terms:
-555 + 555 + -35x + x2 = 0 + 555

Combine like terms: -555 + 555 = 0
0 + -35x + x2 = 0 + 555
-35x + x2 = 0 + 555

Combine like terms: 0 + 555 = 555
-35x + x2 = 555

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = 555 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 555 + 306.25

Combine like terms: 555 + 306.25 = 861.25
306.25 + -35x + x2 = 861.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 861.25

Calculate the square root of the right side: 29.347061182

Break this problem into two subproblems by setting 
(x + -17.5) equal to 29.347061182 and -29.347061182.


Subproblem 1
x + -17.5 = 29.347061182

Simplifying
x + -17.5 = 29.347061182

Reorder the terms:
-17.5 + x = 29.347061182

Solving
-17.5 + x = 29.347061182

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 29.347061182 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 29.347061182 + 17.5
x = 29.347061182 + 17.5

Combine like terms: 29.347061182 + 17.5 = 46.847061182
x = 46.847061182

Simplifying
x = 46.847061182


Subproblem 2
x + -17.5 = -29.347061182

Simplifying
x + -17.5 = -29.347061182

Reorder the terms:
-17.5 + x = -29.347061182

Solving
-17.5 + x = -29.347061182

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -29.347061182 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -29.347061182 + 17.5
x = -29.347061182 + 17.5

Combine like terms: -29.347061182 + 17.5 = -11.847061182
x = -11.847061182

Simplifying
x = -11.847061182


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.847061182, -11.847061182}

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