(3x+5)x=730

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Solution for (3x+5)x=730 equation: 


Simplifying
(3x + 5) * x = 730

Reorder the terms:
(5 + 3x) * x = 730

Reorder the terms for easier multiplication:
x(5 + 3x) = 730
(5 * x + 3x * x) = 730
(5x + 3x2) = 730

Solving
5x + 3x2 = 730

Solving for variable 'x'.

Reorder the terms:
-730 + 5x + 3x2 = 730 + -730

Combine like terms: 730 + -730 = 0
-730 + 5x + 3x2 = 0

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

Divide each side by '3'.
-243.3333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '243.3333333' to each side of the equation.
-243.3333333 + 1.666666667x + 243.3333333 + x2 = 0 + 243.3333333

Reorder the terms:
-243.3333333 + 243.3333333 + 1.666666667x + x2 = 0 + 243.3333333

Combine like terms: -243.3333333 + 243.3333333 = 0.0000000
0.0000000 + 1.666666667x + x2 = 0 + 243.3333333
1.666666667x + x2 = 0 + 243.3333333

Combine like terms: 0 + 243.3333333 = 243.3333333
1.666666667x + x2 = 243.3333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 243.3333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 243.3333333 + 0.6944444447

Combine like terms: 243.3333333 + 0.6944444447 = 244.0277777447
0.6944444447 + 1.666666667x + x2 = 244.0277777447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 244.0277777447

Calculate the square root of the right side: 15.62138847

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 15.62138847 and -15.62138847.


Subproblem 1
x + 0.8333333335 = 15.62138847

Simplifying
x + 0.8333333335 = 15.62138847

Reorder the terms:
0.8333333335 + x = 15.62138847

Solving
0.8333333335 + x = 15.62138847

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 15.62138847 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 15.62138847 + -0.8333333335
x = 15.62138847 + -0.8333333335

Combine like terms: 15.62138847 + -0.8333333335 = 14.7880551365
x = 14.7880551365

Simplifying
x = 14.7880551365


Subproblem 2
x + 0.8333333335 = -15.62138847

Simplifying
x + 0.8333333335 = -15.62138847

Reorder the terms:
0.8333333335 + x = -15.62138847

Solving
0.8333333335 + x = -15.62138847

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -15.62138847 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -15.62138847 + -0.8333333335
x = -15.62138847 + -0.8333333335

Combine like terms: -15.62138847 + -0.8333333335 = -16.4547218035
x = -16.4547218035

Simplifying
x = -16.4547218035


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.7880551365, -16.4547218035}

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