35+x=3x(5+x)

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Solution for 35+x=3x(5+x) equation: 


Simplifying
35 + x = 3x(5 + x)
35 + x = (5 * 3x + x * 3x)
35 + x = (15x + 3x2)

Solving
35 + x = 15x + 3x2

Solving for variable 'x'.

Combine like terms: x + -15x = -14x
35 + -14x + -3x2 = 15x + 3x2 + -15x + -3x2

Reorder the terms:
35 + -14x + -3x2 = 15x + -15x + 3x2 + -3x2

Combine like terms: 15x + -15x = 0
35 + -14x + -3x2 = 0 + 3x2 + -3x2
35 + -14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
35 + -14x + -3x2 = 0

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

Divide each side by '-3'.
-11.66666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 4.666666667x + 11.66666667 + x2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 4.666666667x + x2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 4.666666667x + x2 = 0 + 11.66666667
4.666666667x + x2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
4.666666667x + x2 = 11.66666667

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 11.66666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 11.66666667 + 5.444444448

Combine like terms: 11.66666667 + 5.444444448 = 17.111111118
5.444444448 + 4.666666667x + x2 = 17.111111118

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 17.111111118

Calculate the square root of the right side: 4.136557883

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 4.136557883 and -4.136557883.


Subproblem 1
x + 2.333333334 = 4.136557883

Simplifying
x + 2.333333334 = 4.136557883

Reorder the terms:
2.333333334 + x = 4.136557883

Solving
2.333333334 + x = 4.136557883

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 4.136557883 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 4.136557883 + -2.333333334
x = 4.136557883 + -2.333333334

Combine like terms: 4.136557883 + -2.333333334 = 1.803224549
x = 1.803224549

Simplifying
x = 1.803224549


Subproblem 2
x + 2.333333334 = -4.136557883

Simplifying
x + 2.333333334 = -4.136557883

Reorder the terms:
2.333333334 + x = -4.136557883

Solving
2.333333334 + x = -4.136557883

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -4.136557883 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -4.136557883 + -2.333333334
x = -4.136557883 + -2.333333334

Combine like terms: -4.136557883 + -2.333333334 = -6.469891217
x = -6.469891217

Simplifying
x = -6.469891217


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.803224549, -6.469891217}

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