2x(x+3)=5

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


Simplifying
2x(x + 3) = 5

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

Solving
6x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 6x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 6x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 3x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3x + x2 = 0 + 2.5
3x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3x + x2 = 2.5

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 = 2.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.5 + 2.25

Combine like terms: 2.5 + 2.25 = 4.75
2.25 + 3x + x2 = 4.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.179449472 and -2.179449472.


Subproblem 1
x + 1.5 = 2.179449472

Simplifying
x + 1.5 = 2.179449472

Reorder the terms:
1.5 + x = 2.179449472

Solving
1.5 + x = 2.179449472

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 = 2.179449472 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.179449472 + -1.5
x = 2.179449472 + -1.5

Combine like terms: 2.179449472 + -1.5 = 0.679449472
x = 0.679449472

Simplifying
x = 0.679449472


Subproblem 2
x + 1.5 = -2.179449472

Simplifying
x + 1.5 = -2.179449472

Reorder the terms:
1.5 + x = -2.179449472

Solving
1.5 + x = -2.179449472

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 = -2.179449472 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.179449472 + -1.5
x = -2.179449472 + -1.5

Combine like terms: -2.179449472 + -1.5 = -3.679449472
x = -3.679449472

Simplifying
x = -3.679449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.679449472, -3.679449472}

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