2x+3x(19-x)=45

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Solution for 2x+3x(19-x)=45 equation: 


Simplifying
2x + 3x(19 + -1x) = 45
2x + (19 * 3x + -1x * 3x) = 45
2x + (57x + -3x2) = 45

Combine like terms: 2x + 57x = 59x
59x + -3x2 = 45

Solving
59x + -3x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 59x + -3x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 59x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
15 + -19.66666667x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -19.66666667x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -19.66666667x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -19.66666667x + x2 = 0 + -15
-19.66666667x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-19.66666667x + x2 = -15

The x term is -19.66666667x.  Take half its coefficient (-9.833333335).
Square it (96.69444448) and add it to both sides.

Add '96.69444448' to each side of the equation.
-19.66666667x + 96.69444448 + x2 = -15 + 96.69444448

Reorder the terms:
96.69444448 + -19.66666667x + x2 = -15 + 96.69444448

Combine like terms: -15 + 96.69444448 = 81.69444448
96.69444448 + -19.66666667x + x2 = 81.69444448

Factor a perfect square on the left side:
(x + -9.833333335)(x + -9.833333335) = 81.69444448

Calculate the square root of the right side: 9.038497911

Break this problem into two subproblems by setting 
(x + -9.833333335) equal to 9.038497911 and -9.038497911.


Subproblem 1
x + -9.833333335 = 9.038497911

Simplifying
x + -9.833333335 = 9.038497911

Reorder the terms:
-9.833333335 + x = 9.038497911

Solving
-9.833333335 + x = 9.038497911

Solving for variable 'x'.

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

Add '9.833333335' to each side of the equation.
-9.833333335 + 9.833333335 + x = 9.038497911 + 9.833333335

Combine like terms: -9.833333335 + 9.833333335 = 0.000000000
0.000000000 + x = 9.038497911 + 9.833333335
x = 9.038497911 + 9.833333335

Combine like terms: 9.038497911 + 9.833333335 = 18.871831246
x = 18.871831246

Simplifying
x = 18.871831246


Subproblem 2
x + -9.833333335 = -9.038497911

Simplifying
x + -9.833333335 = -9.038497911

Reorder the terms:
-9.833333335 + x = -9.038497911

Solving
-9.833333335 + x = -9.038497911

Solving for variable 'x'.

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

Add '9.833333335' to each side of the equation.
-9.833333335 + 9.833333335 + x = -9.038497911 + 9.833333335

Combine like terms: -9.833333335 + 9.833333335 = 0.000000000
0.000000000 + x = -9.038497911 + 9.833333335
x = -9.038497911 + 9.833333335

Combine like terms: -9.038497911 + 9.833333335 = 0.794835424
x = 0.794835424

Simplifying
x = 0.794835424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.871831246, 0.794835424}

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