(20+X)(15+X)=450

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Solution for (20+X)(15+X)=450 equation: 


Simplifying
(20 + X)(15 + X) = 450

Multiply (20 + X) * (15 + X)
(20(15 + X) + X(15 + X)) = 450
((15 * 20 + X * 20) + X(15 + X)) = 450
((300 + 20X) + X(15 + X)) = 450
(300 + 20X + (15 * X + X * X)) = 450
(300 + 20X + (15X + X2)) = 450

Combine like terms: 20X + 15X = 35X
(300 + 35X + X2) = 450

Solving
300 + 35X + X2 = 450

Solving for variable 'X'.

Reorder the terms:
300 + -450 + 35X + X2 = 450 + -450

Combine like terms: 300 + -450 = -150
-150 + 35X + X2 = 450 + -450

Combine like terms: 450 + -450 = 0
-150 + 35X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 35X + 150 + X2 = 0 + 150

Reorder the terms:
-150 + 150 + 35X + X2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 35X + X2 = 0 + 150
35X + X2 = 0 + 150

Combine like terms: 0 + 150 = 150
35X + X2 = 150

The X term is 35X.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35X + 306.25 + X2 = 150 + 306.25

Reorder the terms:
306.25 + 35X + X2 = 150 + 306.25

Combine like terms: 150 + 306.25 = 456.25
306.25 + 35X + X2 = 456.25

Factor a perfect square on the left side:
(X + 17.5)(X + 17.5) = 456.25

Calculate the square root of the right side: 21.360009363

Break this problem into two subproblems by setting 
(X + 17.5) equal to 21.360009363 and -21.360009363.


Subproblem 1
X + 17.5 = 21.360009363

Simplifying
X + 17.5 = 21.360009363

Reorder the terms:
17.5 + X = 21.360009363

Solving
17.5 + X = 21.360009363

Solving for variable 'X'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + X = 21.360009363 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + X = 21.360009363 + -17.5
X = 21.360009363 + -17.5

Combine like terms: 21.360009363 + -17.5 = 3.860009363
X = 3.860009363

Simplifying
X = 3.860009363


Subproblem 2
X + 17.5 = -21.360009363

Simplifying
X + 17.5 = -21.360009363

Reorder the terms:
17.5 + X = -21.360009363

Solving
17.5 + X = -21.360009363

Solving for variable 'X'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + X = -21.360009363 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + X = -21.360009363 + -17.5
X = -21.360009363 + -17.5

Combine like terms: -21.360009363 + -17.5 = -38.860009363
X = -38.860009363

Simplifying
X = -38.860009363


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.860009363, -38.860009363}

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