-18x+17=3x(4-x)

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Solution for -18x+17=3x(4-x) equation: 


Simplifying
-18x + 17 = 3x(4 + -1x)

Reorder the terms:
17 + -18x = 3x(4 + -1x)
17 + -18x = (4 * 3x + -1x * 3x)
17 + -18x = (12x + -3x2)

Solving
17 + -18x = 12x + -3x2

Solving for variable 'x'.

Combine like terms: -18x + -12x = -30x
17 + -30x + 3x2 = 12x + -3x2 + -12x + 3x2

Reorder the terms:
17 + -30x + 3x2 = 12x + -12x + -3x2 + 3x2

Combine like terms: 12x + -12x = 0
17 + -30x + 3x2 = 0 + -3x2 + 3x2
17 + -30x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
17 + -30x + 3x2 = 0

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

Divide each side by '3'.
5.666666667 + -10x + x2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -10x + -5.666666667 + x2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -10x + x2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -10x + x2 = 0 + -5.666666667
-10x + x2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-10x + x2 = -5.666666667

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -5.666666667 + 25

Reorder the terms:
25 + -10x + x2 = -5.666666667 + 25

Combine like terms: -5.666666667 + 25 = 19.333333333
25 + -10x + x2 = 19.333333333

Factor a perfect square on the left side:
(x + -5)(x + -5) = 19.333333333

Calculate the square root of the right side: 4.396968653

Break this problem into two subproblems by setting 
(x + -5) equal to 4.396968653 and -4.396968653.


Subproblem 1
x + -5 = 4.396968653

Simplifying
x + -5 = 4.396968653

Reorder the terms:
-5 + x = 4.396968653

Solving
-5 + x = 4.396968653

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.396968653 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.396968653 + 5
x = 4.396968653 + 5

Combine like terms: 4.396968653 + 5 = 9.396968653
x = 9.396968653

Simplifying
x = 9.396968653


Subproblem 2
x + -5 = -4.396968653

Simplifying
x + -5 = -4.396968653

Reorder the terms:
-5 + x = -4.396968653

Solving
-5 + x = -4.396968653

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.396968653 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.396968653 + 5
x = -4.396968653 + 5

Combine like terms: -4.396968653 + 5 = 0.603031347
x = 0.603031347

Simplifying
x = 0.603031347


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.396968653, 0.603031347}

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