-x^2+20x+20=0

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


Simplifying
-1x2 + 20x + 20 = 0

Reorder the terms:
20 + 20x + -1x2 = 0

Solving
20 + 20x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-20 + -20x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 20 + 100

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

Combine like terms: 20 + 100 = 120
100 + -20x + x2 = 120

Factor a perfect square on the left side:
(x + -10)(x + -10) = 120

Calculate the square root of the right side: 10.95445115

Break this problem into two subproblems by setting 
(x + -10) equal to 10.95445115 and -10.95445115.


Subproblem 1
x + -10 = 10.95445115

Simplifying
x + -10 = 10.95445115

Reorder the terms:
-10 + x = 10.95445115

Solving
-10 + x = 10.95445115

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 = 10.95445115 + 10

Combine like terms: -10 + 10 = 0
0 + x = 10.95445115 + 10
x = 10.95445115 + 10

Combine like terms: 10.95445115 + 10 = 20.95445115
x = 20.95445115

Simplifying
x = 20.95445115


Subproblem 2
x + -10 = -10.95445115

Simplifying
x + -10 = -10.95445115

Reorder the terms:
-10 + x = -10.95445115

Solving
-10 + x = -10.95445115

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 = -10.95445115 + 10

Combine like terms: -10 + 10 = 0
0 + x = -10.95445115 + 10
x = -10.95445115 + 10

Combine like terms: -10.95445115 + 10 = -0.95445115
x = -0.95445115

Simplifying
x = -0.95445115


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.95445115, -0.95445115}

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