X*X+20X=400

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Solution for X*X+20X=400 equation: 


Simplifying
X * X + 20X = 400

Multiply X * X
X2 + 20X = 400

Reorder the terms:
20X + X2 = 400

Solving
20X + X2 = 400

Solving for variable 'X'.

Reorder the terms:
-400 + 20X + X2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 20X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 20X + 400 + X2 = 0 + 400

Reorder the terms:
-400 + 400 + 20X + X2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 20X + X2 = 0 + 400
20X + X2 = 0 + 400

Combine like terms: 0 + 400 = 400
20X + X2 = 400

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 = 400 + 100

Reorder the terms:
100 + 20X + X2 = 400 + 100

Combine like terms: 400 + 100 = 500
100 + 20X + X2 = 500

Factor a perfect square on the left side:
(X + 10)(X + 10) = 500

Calculate the square root of the right side: 22.360679775

Break this problem into two subproblems by setting 
(X + 10) equal to 22.360679775 and -22.360679775.


Subproblem 1
X + 10 = 22.360679775

Simplifying
X + 10 = 22.360679775

Reorder the terms:
10 + X = 22.360679775

Solving
10 + X = 22.360679775

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 = 22.360679775 + -10

Combine like terms: 10 + -10 = 0
0 + X = 22.360679775 + -10
X = 22.360679775 + -10

Combine like terms: 22.360679775 + -10 = 12.360679775
X = 12.360679775

Simplifying
X = 12.360679775


Subproblem 2
X + 10 = -22.360679775

Simplifying
X + 10 = -22.360679775

Reorder the terms:
10 + X = -22.360679775

Solving
10 + X = -22.360679775

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 = -22.360679775 + -10

Combine like terms: 10 + -10 = 0
0 + X = -22.360679775 + -10
X = -22.360679775 + -10

Combine like terms: -22.360679775 + -10 = -32.360679775
X = -32.360679775

Simplifying
X = -32.360679775


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {12.360679775, -32.360679775}

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