(2+7)x(12-x)=45

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Solution for (2+7)x(12-x)=45 equation:


Simplifying
(2 + 7) * x(12 + -1x) = 45

Combine like terms: 2 + 7 = 9
(9) * x(12 + -1x) = 45
(12 * 9x + -1x * 9x) = 45
(108x + -9x2) = 45

Solving
108x + -9x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 108x + -9x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 108x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-5 + 12x + -1x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-5 + 12x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + -1x2 = 0

Solving
-5 + 12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -12x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -12x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -12x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -12x + x2 = 0 + -5
-12x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-12x + x2 = -5

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -5 + 36

Reorder the terms:
36 + -12x + x2 = -5 + 36

Combine like terms: -5 + 36 = 31
36 + -12x + x2 = 31

Factor a perfect square on the left side:
(x + -6)(x + -6) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -6) equal to 5.567764363 and -5.567764363.


Subproblem 1
x + -6 = 5.567764363

Simplifying
x + -6 = 5.567764363

Reorder the terms:
-6 + x = 5.567764363

Solving
-6 + x = 5.567764363

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.567764363 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.567764363 + 6
x = 5.567764363 + 6

Combine like terms: 5.567764363 + 6 = 11.567764363
x = 11.567764363

Simplifying
x = 11.567764363


Subproblem 2
x + -6 = -5.567764363

Simplifying
x + -6 = -5.567764363

Reorder the terms:
-6 + x = -5.567764363

Solving
-6 + x = -5.567764363

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.567764363 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.567764363 + 6
x = -5.567764363 + 6

Combine like terms: -5.567764363 + 6 = 0.432235637
x = 0.432235637

Simplifying
x = 0.432235637


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.567764363, 0.432235637}
Solution
x = {11.567764363, 0.432235637}

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