x^2+35x+47=0

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Solution for x^2+35x+47=0 equation: 


Simplifying
x2 + 35x + 47 = 0

Reorder the terms:
47 + 35x + x2 = 0

Solving
47 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 35x + -47 + x2 = 0 + -47

Reorder the terms:
47 + -47 + 35x + x2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 35x + x2 = 0 + -47
35x + x2 = 0 + -47

Combine like terms: 0 + -47 = -47
35x + x2 = -47

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 = -47 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -47 + 306.25

Combine like terms: -47 + 306.25 = 259.25
306.25 + 35x + x2 = 259.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 259.25

Calculate the square root of the right side: 16.101242188

Break this problem into two subproblems by setting 
(x + 17.5) equal to 16.101242188 and -16.101242188.


Subproblem 1
x + 17.5 = 16.101242188

Simplifying
x + 17.5 = 16.101242188

Reorder the terms:
17.5 + x = 16.101242188

Solving
17.5 + x = 16.101242188

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 = 16.101242188 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 16.101242188 + -17.5
x = 16.101242188 + -17.5

Combine like terms: 16.101242188 + -17.5 = -1.398757812
x = -1.398757812

Simplifying
x = -1.398757812


Subproblem 2
x + 17.5 = -16.101242188

Simplifying
x + 17.5 = -16.101242188

Reorder the terms:
17.5 + x = -16.101242188

Solving
17.5 + x = -16.101242188

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 = -16.101242188 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -16.101242188 + -17.5
x = -16.101242188 + -17.5

Combine like terms: -16.101242188 + -17.5 = -33.601242188
x = -33.601242188

Simplifying
x = -33.601242188


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.398757812, -33.601242188}

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