3x(x+3)=7

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Solution for 3x(x+3)=7 equation: 


Simplifying
3x(x + 3) = 7

Reorder the terms:
3x(3 + x) = 7
(3 * 3x + x * 3x) = 7
(9x + 3x2) = 7

Solving
9x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 9x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 9x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + 3x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 3x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 3x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + 2.333333333
3x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
3x + x2 = 2.333333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2.333333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.333333333 + 2.25

Combine like terms: 2.333333333 + 2.25 = 4.583333333
2.25 + 3x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
x + 1.5 = 2.140872096

Simplifying
x + 1.5 = 2.140872096

Reorder the terms:
1.5 + x = 2.140872096

Solving
1.5 + x = 2.140872096

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.140872096 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.140872096 + -1.5
x = 2.140872096 + -1.5

Combine like terms: 2.140872096 + -1.5 = 0.640872096
x = 0.640872096

Simplifying
x = 0.640872096


Subproblem 2
x + 1.5 = -2.140872096

Simplifying
x + 1.5 = -2.140872096

Reorder the terms:
1.5 + x = -2.140872096

Solving
1.5 + x = -2.140872096

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.140872096 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.140872096 + -1.5
x = -2.140872096 + -1.5

Combine like terms: -2.140872096 + -1.5 = -3.640872096
x = -3.640872096

Simplifying
x = -3.640872096


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.640872096, -3.640872096}

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