3x(5+x)=17

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Solution for 3x(5+x)=17 equation: 


Simplifying
3x(5 + x) = 17
(5 * 3x + x * 3x) = 17
(15x + 3x2) = 17

Solving
15x + 3x2 = 17

Solving for variable 'x'.

Reorder the terms:
-17 + 15x + 3x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + 15x + 3x2 = 0

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

Divide each side by '3'.
-5.666666667 + 5x + x2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + 5x + 5.666666667 + x2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + 5x + x2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + 5x + x2 = 0 + 5.666666667
5x + x2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
5x + x2 = 5.666666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 5.666666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 5.666666667 + 6.25

Combine like terms: 5.666666667 + 6.25 = 11.916666667
6.25 + 5x + x2 = 11.916666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11.916666667

Calculate the square root of the right side: 3.45205253

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.45205253 and -3.45205253.


Subproblem 1
x + 2.5 = 3.45205253

Simplifying
x + 2.5 = 3.45205253

Reorder the terms:
2.5 + x = 3.45205253

Solving
2.5 + x = 3.45205253

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.45205253 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.45205253 + -2.5
x = 3.45205253 + -2.5

Combine like terms: 3.45205253 + -2.5 = 0.95205253
x = 0.95205253

Simplifying
x = 0.95205253


Subproblem 2
x + 2.5 = -3.45205253

Simplifying
x + 2.5 = -3.45205253

Reorder the terms:
2.5 + x = -3.45205253

Solving
2.5 + x = -3.45205253

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.45205253 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.45205253 + -2.5
x = -3.45205253 + -2.5

Combine like terms: -3.45205253 + -2.5 = -5.95205253
x = -5.95205253

Simplifying
x = -5.95205253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.95205253, -5.95205253}

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