x^2+35x-17=0

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Solution for x^2+35x-17=0 equation: 


Simplifying
x2 + 35x + -17 = 0

Reorder the terms:
-17 + 35x + x2 = 0

Solving
-17 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 35x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 35x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 35x + x2 = 0 + 17
35x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
35x + x2 = 17

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 = 17 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 17 + 306.25

Combine like terms: 17 + 306.25 = 323.25
306.25 + 35x + x2 = 323.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 323.25

Calculate the square root of the right side: 17.979154596

Break this problem into two subproblems by setting 
(x + 17.5) equal to 17.979154596 and -17.979154596.


Subproblem 1
x + 17.5 = 17.979154596

Simplifying
x + 17.5 = 17.979154596

Reorder the terms:
17.5 + x = 17.979154596

Solving
17.5 + x = 17.979154596

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 = 17.979154596 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 17.979154596 + -17.5
x = 17.979154596 + -17.5

Combine like terms: 17.979154596 + -17.5 = 0.479154596
x = 0.479154596

Simplifying
x = 0.479154596


Subproblem 2
x + 17.5 = -17.979154596

Simplifying
x + 17.5 = -17.979154596

Reorder the terms:
17.5 + x = -17.979154596

Solving
17.5 + x = -17.979154596

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 = -17.979154596 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -17.979154596 + -17.5
x = -17.979154596 + -17.5

Combine like terms: -17.979154596 + -17.5 = -35.479154596
x = -35.479154596

Simplifying
x = -35.479154596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.479154596, -35.479154596}

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