x^2+20x+94=0

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Solution for x^2+20x+94=0 equation: 


Simplifying
x2 + 20x + 94 = 0

Reorder the terms:
94 + 20x + x2 = 0

Solving
94 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-94' to each side of the equation.
94 + 20x + -94 + x2 = 0 + -94

Reorder the terms:
94 + -94 + 20x + x2 = 0 + -94

Combine like terms: 94 + -94 = 0
0 + 20x + x2 = 0 + -94
20x + x2 = 0 + -94

Combine like terms: 0 + -94 = -94
20x + x2 = -94

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -94 + 100

Reorder the terms:
100 + 20x + x2 = -94 + 100

Combine like terms: -94 + 100 = 6
100 + 20x + x2 = 6

Factor a perfect square on the left side:
(x + 10)(x + 10) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 10) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 10 = 2.449489743

Simplifying
x + 10 = 2.449489743

Reorder the terms:
10 + x = 2.449489743

Solving
10 + x = 2.449489743

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = 2.449489743 + -10

Combine like terms: 10 + -10 = 0
0 + x = 2.449489743 + -10
x = 2.449489743 + -10

Combine like terms: 2.449489743 + -10 = -7.550510257
x = -7.550510257

Simplifying
x = -7.550510257


Subproblem 2
x + 10 = -2.449489743

Simplifying
x + 10 = -2.449489743

Reorder the terms:
10 + x = -2.449489743

Solving
10 + x = -2.449489743

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = -2.449489743 + -10

Combine like terms: 10 + -10 = 0
0 + x = -2.449489743 + -10
x = -2.449489743 + -10

Combine like terms: -2.449489743 + -10 = -12.449489743
x = -12.449489743

Simplifying
x = -12.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.550510257, -12.449489743}

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