5x(3x+13)=46

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Solution for 5x(3x+13)=46 equation: 


Simplifying
5x(3x + 13) = 46

Reorder the terms:
5x(13 + 3x) = 46
(13 * 5x + 3x * 5x) = 46
(65x + 15x2) = 46

Solving
65x + 15x2 = 46

Solving for variable 'x'.

Reorder the terms:
-46 + 65x + 15x2 = 46 + -46

Combine like terms: 46 + -46 = 0
-46 + 65x + 15x2 = 0

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

Divide each side by '15'.
-3.066666667 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '3.066666667' to each side of the equation.
-3.066666667 + 4.333333333x + 3.066666667 + x2 = 0 + 3.066666667

Reorder the terms:
-3.066666667 + 3.066666667 + 4.333333333x + x2 = 0 + 3.066666667

Combine like terms: -3.066666667 + 3.066666667 = 0.000000000
0.000000000 + 4.333333333x + x2 = 0 + 3.066666667
4.333333333x + x2 = 0 + 3.066666667

Combine like terms: 0 + 3.066666667 = 3.066666667
4.333333333x + x2 = 3.066666667

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 3.066666667 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 3.066666667 + 4.694444446

Combine like terms: 3.066666667 + 4.694444446 = 7.761111113
4.694444446 + 4.333333333x + x2 = 7.761111113

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 7.761111113

Calculate the square root of the right side: 2.785877081

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 2.785877081 and -2.785877081.


Subproblem 1
x + 2.166666667 = 2.785877081

Simplifying
x + 2.166666667 = 2.785877081

Reorder the terms:
2.166666667 + x = 2.785877081

Solving
2.166666667 + x = 2.785877081

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 2.785877081 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 2.785877081 + -2.166666667
x = 2.785877081 + -2.166666667

Combine like terms: 2.785877081 + -2.166666667 = 0.619210414
x = 0.619210414

Simplifying
x = 0.619210414


Subproblem 2
x + 2.166666667 = -2.785877081

Simplifying
x + 2.166666667 = -2.785877081

Reorder the terms:
2.166666667 + x = -2.785877081

Solving
2.166666667 + x = -2.785877081

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -2.785877081 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -2.785877081 + -2.166666667
x = -2.785877081 + -2.166666667

Combine like terms: -2.785877081 + -2.166666667 = -4.952543748
x = -4.952543748

Simplifying
x = -4.952543748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.619210414, -4.952543748}

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