3x+2x(23-x)=57

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Solution for 3x+2x(23-x)=57 equation: 


Simplifying
3x + 2x(23 + -1x) = 57
3x + (23 * 2x + -1x * 2x) = 57
3x + (46x + -2x2) = 57

Combine like terms: 3x + 46x = 49x
49x + -2x2 = 57

Solving
49x + -2x2 = 57

Solving for variable 'x'.

Reorder the terms:
-57 + 49x + -2x2 = 57 + -57

Combine like terms: 57 + -57 = 0
-57 + 49x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
28.5 + -24.5x + x2 = 0

Move the constant term to the right:

Add '-28.5' to each side of the equation.
28.5 + -24.5x + -28.5 + x2 = 0 + -28.5

Reorder the terms:
28.5 + -28.5 + -24.5x + x2 = 0 + -28.5

Combine like terms: 28.5 + -28.5 = 0.0
0.0 + -24.5x + x2 = 0 + -28.5
-24.5x + x2 = 0 + -28.5

Combine like terms: 0 + -28.5 = -28.5
-24.5x + x2 = -28.5

The x term is -24.5x.  Take half its coefficient (-12.25).
Square it (150.0625) and add it to both sides.

Add '150.0625' to each side of the equation.
-24.5x + 150.0625 + x2 = -28.5 + 150.0625

Reorder the terms:
150.0625 + -24.5x + x2 = -28.5 + 150.0625

Combine like terms: -28.5 + 150.0625 = 121.5625
150.0625 + -24.5x + x2 = 121.5625

Factor a perfect square on the left side:
(x + -12.25)(x + -12.25) = 121.5625

Calculate the square root of the right side: 11.025538536

Break this problem into two subproblems by setting 
(x + -12.25) equal to 11.025538536 and -11.025538536.


Subproblem 1
x + -12.25 = 11.025538536

Simplifying
x + -12.25 = 11.025538536

Reorder the terms:
-12.25 + x = 11.025538536

Solving
-12.25 + x = 11.025538536

Solving for variable 'x'.

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

Add '12.25' to each side of the equation.
-12.25 + 12.25 + x = 11.025538536 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + x = 11.025538536 + 12.25
x = 11.025538536 + 12.25

Combine like terms: 11.025538536 + 12.25 = 23.275538536
x = 23.275538536

Simplifying
x = 23.275538536


Subproblem 2
x + -12.25 = -11.025538536

Simplifying
x + -12.25 = -11.025538536

Reorder the terms:
-12.25 + x = -11.025538536

Solving
-12.25 + x = -11.025538536

Solving for variable 'x'.

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

Add '12.25' to each side of the equation.
-12.25 + 12.25 + x = -11.025538536 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + x = -11.025538536 + 12.25
x = -11.025538536 + 12.25

Combine like terms: -11.025538536 + 12.25 = 1.224461464
x = 1.224461464

Simplifying
x = 1.224461464


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.275538536, 1.224461464}

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