x^2-35x-275=0

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Solution for x^2-35x-275=0 equation: 


Simplifying
x2 + -35x + -275 = 0

Reorder the terms:
-275 + -35x + x2 = 0

Solving
-275 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '275' to each side of the equation.
-275 + -35x + 275 + x2 = 0 + 275

Reorder the terms:
-275 + 275 + -35x + x2 = 0 + 275

Combine like terms: -275 + 275 = 0
0 + -35x + x2 = 0 + 275
-35x + x2 = 0 + 275

Combine like terms: 0 + 275 = 275
-35x + x2 = 275

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 = 275 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 275 + 306.25

Combine like terms: 275 + 306.25 = 581.25
306.25 + -35x + x2 = 581.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 581.25

Calculate the square root of the right side: 24.109126902

Break this problem into two subproblems by setting 
(x + -17.5) equal to 24.109126902 and -24.109126902.


Subproblem 1
x + -17.5 = 24.109126902

Simplifying
x + -17.5 = 24.109126902

Reorder the terms:
-17.5 + x = 24.109126902

Solving
-17.5 + x = 24.109126902

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 = 24.109126902 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 24.109126902 + 17.5
x = 24.109126902 + 17.5

Combine like terms: 24.109126902 + 17.5 = 41.609126902
x = 41.609126902

Simplifying
x = 41.609126902


Subproblem 2
x + -17.5 = -24.109126902

Simplifying
x + -17.5 = -24.109126902

Reorder the terms:
-17.5 + x = -24.109126902

Solving
-17.5 + x = -24.109126902

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 = -24.109126902 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -24.109126902 + 17.5
x = -24.109126902 + 17.5

Combine like terms: -24.109126902 + 17.5 = -6.609126902
x = -6.609126902

Simplifying
x = -6.609126902


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.609126902, -6.609126902}

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