(2)(x^2+3x)=150

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Solution for (2)(x^2+3x)=150 equation: 


Simplifying
(2)(x2 + 3x) = 150

Reorder the terms:
2(3x + x2) = 150
(3x * 2 + x2 * 2) = 150
(6x + 2x2) = 150

Solving
6x + 2x2 = 150

Solving for variable 'x'.

Reorder the terms:
-150 + 6x + 2x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-75 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + 3x + x2 = 0

Solving
-75 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 3x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 3x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 3x + x2 = 0 + 75
3x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
3x + x2 = 75

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 = 75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 75 + 2.25

Combine like terms: 75 + 2.25 = 77.25
2.25 + 3x + x2 = 77.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 77.25

Calculate the square root of the right side: 8.789197916

Break this problem into two subproblems by setting 
(x + 1.5) equal to 8.789197916 and -8.789197916.


Subproblem 1
x + 1.5 = 8.789197916

Simplifying
x + 1.5 = 8.789197916

Reorder the terms:
1.5 + x = 8.789197916

Solving
1.5 + x = 8.789197916

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 = 8.789197916 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 8.789197916 + -1.5
x = 8.789197916 + -1.5

Combine like terms: 8.789197916 + -1.5 = 7.289197916
x = 7.289197916

Simplifying
x = 7.289197916


Subproblem 2
x + 1.5 = -8.789197916

Simplifying
x + 1.5 = -8.789197916

Reorder the terms:
1.5 + x = -8.789197916

Solving
1.5 + x = -8.789197916

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 = -8.789197916 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -8.789197916 + -1.5
x = -8.789197916 + -1.5

Combine like terms: -8.789197916 + -1.5 = -10.289197916
x = -10.289197916

Simplifying
x = -10.289197916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.289197916, -10.289197916}
Solution
x = {7.289197916, -10.289197916}

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