x^2+35x+16=0

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Solution for x^2+35x+16=0 equation: 


Simplifying
x2 + 35x + 16 = 0

Reorder the terms:
16 + 35x + x2 = 0

Solving
16 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 35x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 35x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 35x + x2 = 0 + -16
35x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
35x + x2 = -16

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 = -16 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -16 + 306.25

Combine like terms: -16 + 306.25 = 290.25
306.25 + 35x + x2 = 290.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 290.25

Calculate the square root of the right side: 17.036725037

Break this problem into two subproblems by setting 
(x + 17.5) equal to 17.036725037 and -17.036725037.


Subproblem 1
x + 17.5 = 17.036725037

Simplifying
x + 17.5 = 17.036725037

Reorder the terms:
17.5 + x = 17.036725037

Solving
17.5 + x = 17.036725037

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 = 17.036725037 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 17.036725037 + -17.5
x = 17.036725037 + -17.5

Combine like terms: 17.036725037 + -17.5 = -0.463274963
x = -0.463274963

Simplifying
x = -0.463274963


Subproblem 2
x + 17.5 = -17.036725037

Simplifying
x + 17.5 = -17.036725037

Reorder the terms:
17.5 + x = -17.036725037

Solving
17.5 + x = -17.036725037

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 = -17.036725037 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -17.036725037 + -17.5
x = -17.036725037 + -17.5

Combine like terms: -17.036725037 + -17.5 = -34.536725037
x = -34.536725037

Simplifying
x = -34.536725037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.463274963, -34.536725037}

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