x*x+20x-200=0

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Solution for x*x+20x-200=0 equation: 


Simplifying
x * x + 20x + -200 = 0

Multiply x * x
x2 + 20x + -200 = 0

Reorder the terms:
-200 + 20x + x2 = 0

Solving
-200 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 20x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 20x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 20x + x2 = 0 + 200
20x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
20x + x2 = 200

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 = 200 + 100

Reorder the terms:
100 + 20x + x2 = 200 + 100

Combine like terms: 200 + 100 = 300
100 + 20x + x2 = 300

Factor a perfect square on the left side:
(x + 10)(x + 10) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + 10) equal to 17.320508076 and -17.320508076.


Subproblem 1
x + 10 = 17.320508076

Simplifying
x + 10 = 17.320508076

Reorder the terms:
10 + x = 17.320508076

Solving
10 + x = 17.320508076

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 = 17.320508076 + -10

Combine like terms: 10 + -10 = 0
0 + x = 17.320508076 + -10
x = 17.320508076 + -10

Combine like terms: 17.320508076 + -10 = 7.320508076
x = 7.320508076

Simplifying
x = 7.320508076


Subproblem 2
x + 10 = -17.320508076

Simplifying
x + 10 = -17.320508076

Reorder the terms:
10 + x = -17.320508076

Solving
10 + x = -17.320508076

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 = -17.320508076 + -10

Combine like terms: 10 + -10 = 0
0 + x = -17.320508076 + -10
x = -17.320508076 + -10

Combine like terms: -17.320508076 + -10 = -27.320508076
x = -27.320508076

Simplifying
x = -27.320508076


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.320508076, -27.320508076}

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