x^2+20x+100=69

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Solution for x^2+20x+100=69 equation: 


Simplifying
x2 + 20x + 100 = 69

Reorder the terms:
100 + 20x + x2 = 69

Solving
100 + 20x + x2 = 69

Solving for variable 'x'.

Reorder the terms:
100 + -69 + 20x + x2 = 69 + -69

Combine like terms: 100 + -69 = 31
31 + 20x + x2 = 69 + -69

Combine like terms: 69 + -69 = 0
31 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + 20x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + 20x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + 20x + x2 = 0 + -31
20x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
20x + x2 = -31

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 = -31 + 100

Reorder the terms:
100 + 20x + x2 = -31 + 100

Combine like terms: -31 + 100 = 69
100 + 20x + x2 = 69

Factor a perfect square on the left side:
(x + 10)(x + 10) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + 10) equal to 8.306623863 and -8.306623863.


Subproblem 1
x + 10 = 8.306623863

Simplifying
x + 10 = 8.306623863

Reorder the terms:
10 + x = 8.306623863

Solving
10 + x = 8.306623863

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 = 8.306623863 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.306623863 + -10
x = 8.306623863 + -10

Combine like terms: 8.306623863 + -10 = -1.693376137
x = -1.693376137

Simplifying
x = -1.693376137


Subproblem 2
x + 10 = -8.306623863

Simplifying
x + 10 = -8.306623863

Reorder the terms:
10 + x = -8.306623863

Solving
10 + x = -8.306623863

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 = -8.306623863 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.306623863 + -10
x = -8.306623863 + -10

Combine like terms: -8.306623863 + -10 = -18.306623863
x = -18.306623863

Simplifying
x = -18.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.693376137, -18.306623863}

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