(50+X)(10+X)=120

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Solution for (50+X)(10+X)=120 equation: 


Simplifying
(50 + X)(10 + X) = 120

Multiply (50 + X) * (10 + X)
(50(10 + X) + X(10 + X)) = 120
((10 * 50 + X * 50) + X(10 + X)) = 120
((500 + 50X) + X(10 + X)) = 120
(500 + 50X + (10 * X + X * X)) = 120
(500 + 50X + (10X + X2)) = 120

Combine like terms: 50X + 10X = 60X
(500 + 60X + X2) = 120

Solving
500 + 60X + X2 = 120

Solving for variable 'X'.

Reorder the terms:
500 + -120 + 60X + X2 = 120 + -120

Combine like terms: 500 + -120 = 380
380 + 60X + X2 = 120 + -120

Combine like terms: 120 + -120 = 0
380 + 60X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-380' to each side of the equation.
380 + 60X + -380 + X2 = 0 + -380

Reorder the terms:
380 + -380 + 60X + X2 = 0 + -380

Combine like terms: 380 + -380 = 0
0 + 60X + X2 = 0 + -380
60X + X2 = 0 + -380

Combine like terms: 0 + -380 = -380
60X + X2 = -380

The X term is 60X.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60X + 900 + X2 = -380 + 900

Reorder the terms:
900 + 60X + X2 = -380 + 900

Combine like terms: -380 + 900 = 520
900 + 60X + X2 = 520

Factor a perfect square on the left side:
(X + 30)(X + 30) = 520

Calculate the square root of the right side: 22.803508502

Break this problem into two subproblems by setting 
(X + 30) equal to 22.803508502 and -22.803508502.


Subproblem 1
X + 30 = 22.803508502

Simplifying
X + 30 = 22.803508502

Reorder the terms:
30 + X = 22.803508502

Solving
30 + X = 22.803508502

Solving for variable 'X'.

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

Add '-30' to each side of the equation.
30 + -30 + X = 22.803508502 + -30

Combine like terms: 30 + -30 = 0
0 + X = 22.803508502 + -30
X = 22.803508502 + -30

Combine like terms: 22.803508502 + -30 = -7.196491498
X = -7.196491498

Simplifying
X = -7.196491498


Subproblem 2
X + 30 = -22.803508502

Simplifying
X + 30 = -22.803508502

Reorder the terms:
30 + X = -22.803508502

Solving
30 + X = -22.803508502

Solving for variable 'X'.

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

Add '-30' to each side of the equation.
30 + -30 + X = -22.803508502 + -30

Combine like terms: 30 + -30 = 0
0 + X = -22.803508502 + -30
X = -22.803508502 + -30

Combine like terms: -22.803508502 + -30 = -52.803508502
X = -52.803508502

Simplifying
X = -52.803508502


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-7.196491498, -52.803508502}

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