(10+(0.5X))X=112

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Solution for (10+(0.5X))X=112 equation: 


Simplifying
(10 + (0.5X)) * X = 112

Reorder the terms for easier multiplication:
X(10 + (0.5X)) = 112
(10 * X + (0.5X) * X) = 112
(10X + 0.5X2) = 112

Solving
10X + 0.5X2 = 112

Solving for variable 'X'.

Reorder the terms:
-112 + 10X + 0.5X2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + 10X + 0.5X2 = 0

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

Divide each side by '0.5'.
-224 + 20X + X2 = 0

Move the constant term to the right:

Add '224' to each side of the equation.
-224 + 20X + 224 + X2 = 0 + 224

Reorder the terms:
-224 + 224 + 20X + X2 = 0 + 224

Combine like terms: -224 + 224 = 0
0 + 20X + X2 = 0 + 224
20X + X2 = 0 + 224

Combine like terms: 0 + 224 = 224
20X + X2 = 224

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 = 224 + 100

Reorder the terms:
100 + 20X + X2 = 224 + 100

Combine like terms: 224 + 100 = 324
100 + 20X + X2 = 324

Factor a perfect square on the left side:
(X + 10)(X + 10) = 324

Calculate the square root of the right side: 18

Break this problem into two subproblems by setting 
(X + 10) equal to 18 and -18.


Subproblem 1
X + 10 = 18

Simplifying
X + 10 = 18

Reorder the terms:
10 + X = 18

Solving
10 + X = 18

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 = 18 + -10

Combine like terms: 10 + -10 = 0
0 + X = 18 + -10
X = 18 + -10

Combine like terms: 18 + -10 = 8
X = 8

Simplifying
X = 8


Subproblem 2
X + 10 = -18

Simplifying
X + 10 = -18

Reorder the terms:
10 + X = -18

Solving
10 + X = -18

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 = -18 + -10

Combine like terms: 10 + -10 = 0
0 + X = -18 + -10
X = -18 + -10

Combine like terms: -18 + -10 = -28
X = -28

Simplifying
X = -28


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {8, -28}

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