x^2-35x-960.80=0

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Solution for x^2-35x-960.80=0 equation: 


Simplifying
x2 + -35x + -960.80 = 0

Reorder the terms:
-960.80 + -35x + x2 = 0

Solving
-960.80 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '960.80' to each side of the equation.
-960.80 + -35x + 960.80 + x2 = 0 + 960.80

Reorder the terms:
-960.80 + 960.80 + -35x + x2 = 0 + 960.80

Combine like terms: -960.80 + 960.80 = 0.00
0.00 + -35x + x2 = 0 + 960.80
-35x + x2 = 0 + 960.80

Combine like terms: 0 + 960.80 = 960.8
-35x + x2 = 960.8

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 = 960.8 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 960.8 + 306.25

Combine like terms: 960.8 + 306.25 = 1267.05
306.25 + -35x + x2 = 1267.05

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 1267.05

Calculate the square root of the right side: 35.595645801

Break this problem into two subproblems by setting 
(x + -17.5) equal to 35.595645801 and -35.595645801.


Subproblem 1
x + -17.5 = 35.595645801

Simplifying
x + -17.5 = 35.595645801

Reorder the terms:
-17.5 + x = 35.595645801

Solving
-17.5 + x = 35.595645801

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 = 35.595645801 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 35.595645801 + 17.5
x = 35.595645801 + 17.5

Combine like terms: 35.595645801 + 17.5 = 53.095645801
x = 53.095645801

Simplifying
x = 53.095645801


Subproblem 2
x + -17.5 = -35.595645801

Simplifying
x + -17.5 = -35.595645801

Reorder the terms:
-17.5 + x = -35.595645801

Solving
-17.5 + x = -35.595645801

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 = -35.595645801 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -35.595645801 + 17.5
x = -35.595645801 + 17.5

Combine like terms: -35.595645801 + 17.5 = -18.095645801
x = -18.095645801

Simplifying
x = -18.095645801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.095645801, -18.095645801}

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