3x(2x+5)=39

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Solution for 3x(2x+5)=39 equation: 


Simplifying
3x(2x + 5) = 39

Reorder the terms:
3x(5 + 2x) = 39
(5 * 3x + 2x * 3x) = 39
(15x + 6x2) = 39

Solving
15x + 6x2 = 39

Solving for variable 'x'.

Reorder the terms:
-39 + 15x + 6x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-39 + 15x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + 5x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-13 + 5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-13 + 5x + 2x2 = 0

Solving
-13 + 5x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 2.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 2.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 2.5x + x2 = 0 + 6.5
2.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
2.5x + x2 = 6.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 6.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 6.5 + 1.5625

Combine like terms: 6.5 + 1.5625 = 8.0625
1.5625 + 2.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.839454173 and -2.839454173.


Subproblem 1
x + 1.25 = 2.839454173

Simplifying
x + 1.25 = 2.839454173

Reorder the terms:
1.25 + x = 2.839454173

Solving
1.25 + x = 2.839454173

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 2.839454173 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.839454173 + -1.25
x = 2.839454173 + -1.25

Combine like terms: 2.839454173 + -1.25 = 1.589454173
x = 1.589454173

Simplifying
x = 1.589454173


Subproblem 2
x + 1.25 = -2.839454173

Simplifying
x + 1.25 = -2.839454173

Reorder the terms:
1.25 + x = -2.839454173

Solving
1.25 + x = -2.839454173

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -2.839454173 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.839454173 + -1.25
x = -2.839454173 + -1.25

Combine like terms: -2.839454173 + -1.25 = -4.089454173
x = -4.089454173

Simplifying
x = -4.089454173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.589454173, -4.089454173}
Solution
x = {1.589454173, -4.089454173}

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