x^2-35x-110=0

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Solution for x^2-35x-110=0 equation: 


Simplifying
x2 + -35x + -110 = 0

Reorder the terms:
-110 + -35x + x2 = 0

Solving
-110 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + -35x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + -35x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + -35x + x2 = 0 + 110
-35x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
-35x + x2 = 110

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 = 110 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 110 + 306.25

Combine like terms: 110 + 306.25 = 416.25
306.25 + -35x + x2 = 416.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 416.25

Calculate the square root of the right side: 20.402205763

Break this problem into two subproblems by setting 
(x + -17.5) equal to 20.402205763 and -20.402205763.


Subproblem 1
x + -17.5 = 20.402205763

Simplifying
x + -17.5 = 20.402205763

Reorder the terms:
-17.5 + x = 20.402205763

Solving
-17.5 + x = 20.402205763

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 = 20.402205763 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 20.402205763 + 17.5
x = 20.402205763 + 17.5

Combine like terms: 20.402205763 + 17.5 = 37.902205763
x = 37.902205763

Simplifying
x = 37.902205763


Subproblem 2
x + -17.5 = -20.402205763

Simplifying
x + -17.5 = -20.402205763

Reorder the terms:
-17.5 + x = -20.402205763

Solving
-17.5 + x = -20.402205763

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 = -20.402205763 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -20.402205763 + 17.5
x = -20.402205763 + 17.5

Combine like terms: -20.402205763 + 17.5 = -2.902205763
x = -2.902205763

Simplifying
x = -2.902205763


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.902205763, -2.902205763}

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