5x(3x+2)=14+5

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Solution for 5x(3x+2)=14+5 equation: 


Simplifying
5x(3x + 2) = 14 + 5

Reorder the terms:
5x(2 + 3x) = 14 + 5
(2 * 5x + 3x * 5x) = 14 + 5
(10x + 15x2) = 14 + 5

Combine like terms: 14 + 5 = 19
10x + 15x2 = 19

Solving
10x + 15x2 = 19

Solving for variable 'x'.

Reorder the terms:
-19 + 10x + 15x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + 10x + 15x2 = 0

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

Divide each side by '15'.
-1.266666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.266666667' to each side of the equation.
-1.266666667 + 0.6666666667x + 1.266666667 + x2 = 0 + 1.266666667

Reorder the terms:
-1.266666667 + 1.266666667 + 0.6666666667x + x2 = 0 + 1.266666667

Combine like terms: -1.266666667 + 1.266666667 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.266666667
0.6666666667x + x2 = 0 + 1.266666667

Combine like terms: 0 + 1.266666667 = 1.266666667
0.6666666667x + x2 = 1.266666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.266666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.266666667 + 0.1111111112

Combine like terms: 1.266666667 + 0.1111111112 = 1.3777777782
0.1111111112 + 0.6666666667x + x2 = 1.3777777782

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.3777777782

Calculate the square root of the right side: 1.173787791

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.173787791 and -1.173787791.


Subproblem 1
x + 0.3333333334 = 1.173787791

Simplifying
x + 0.3333333334 = 1.173787791

Reorder the terms:
0.3333333334 + x = 1.173787791

Solving
0.3333333334 + x = 1.173787791

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.173787791 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.173787791 + -0.3333333334
x = 1.173787791 + -0.3333333334

Combine like terms: 1.173787791 + -0.3333333334 = 0.8404544576
x = 0.8404544576

Simplifying
x = 0.8404544576


Subproblem 2
x + 0.3333333334 = -1.173787791

Simplifying
x + 0.3333333334 = -1.173787791

Reorder the terms:
0.3333333334 + x = -1.173787791

Solving
0.3333333334 + x = -1.173787791

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.173787791 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.173787791 + -0.3333333334
x = -1.173787791 + -0.3333333334

Combine like terms: -1.173787791 + -0.3333333334 = -1.5071211244
x = -1.5071211244

Simplifying
x = -1.5071211244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8404544576, -1.5071211244}

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