x^2+35x-880=0

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Solution for x^2+35x-880=0 equation:


Simplifying
x2 + 35x + -880 = 0

Reorder the terms:
-880 + 35x + x2 = 0

Solving
-880 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '880' to each side of the equation.
-880 + 35x + 880 + x2 = 0 + 880

Reorder the terms:
-880 + 880 + 35x + x2 = 0 + 880

Combine like terms: -880 + 880 = 0
0 + 35x + x2 = 0 + 880
35x + x2 = 0 + 880

Combine like terms: 0 + 880 = 880
35x + x2 = 880

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 = 880 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 880 + 306.25

Combine like terms: 880 + 306.25 = 1186.25
306.25 + 35x + x2 = 1186.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 1186.25

Calculate the square root of the right side: 34.441980199

Break this problem into two subproblems by setting 
(x + 17.5) equal to 34.441980199 and -34.441980199.


Subproblem 1
x + 17.5 = 34.441980199

Simplifying
x + 17.5 = 34.441980199

Reorder the terms:
17.5 + x = 34.441980199

Solving
17.5 + x = 34.441980199

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 = 34.441980199 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 34.441980199 + -17.5
x = 34.441980199 + -17.5

Combine like terms: 34.441980199 + -17.5 = 16.941980199
x = 16.941980199

Simplifying
x = 16.941980199


Subproblem 2
x + 17.5 = -34.441980199

Simplifying
x + 17.5 = -34.441980199

Reorder the terms:
17.5 + x = -34.441980199

Solving
17.5 + x = -34.441980199

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 = -34.441980199 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -34.441980199 + -17.5
x = -34.441980199 + -17.5

Combine like terms: -34.441980199 + -17.5 = -51.941980199
x = -51.941980199

Simplifying
x = -51.941980199


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.941980199, -51.941980199}

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