x(1.2x-7)=300

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Solution for x(1.2x-7)=300 equation: 


Simplifying
x(1.2x + -7) = 300

Reorder the terms:
x(-7 + 1.2x) = 300
(-7 * x + 1.2x * x) = 300
(-7x + 1.2x2) = 300

Solving
-7x + 1.2x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + -7x + 1.2x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + -7x + 1.2x2 = 0

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

Divide each side by '1.2'.
-250 + -5.833333333x + x2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -5.833333333x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + -5.833333333x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -5.833333333x + x2 = 0 + 250
-5.833333333x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
-5.833333333x + x2 = 250

The x term is -5.833333333x.  Take half its coefficient (-2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
-5.833333333x + 8.506944446 + x2 = 250 + 8.506944446

Reorder the terms:
8.506944446 + -5.833333333x + x2 = 250 + 8.506944446

Combine like terms: 250 + 8.506944446 = 258.506944446
8.506944446 + -5.833333333x + x2 = 258.506944446

Factor a perfect square on the left side:
(x + -2.916666667)(x + -2.916666667) = 258.506944446

Calculate the square root of the right side: 16.078151151

Break this problem into two subproblems by setting 
(x + -2.916666667) equal to 16.078151151 and -16.078151151.


Subproblem 1
x + -2.916666667 = 16.078151151

Simplifying
x + -2.916666667 = 16.078151151

Reorder the terms:
-2.916666667 + x = 16.078151151

Solving
-2.916666667 + x = 16.078151151

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = 16.078151151 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = 16.078151151 + 2.916666667
x = 16.078151151 + 2.916666667

Combine like terms: 16.078151151 + 2.916666667 = 18.994817818
x = 18.994817818

Simplifying
x = 18.994817818


Subproblem 2
x + -2.916666667 = -16.078151151

Simplifying
x + -2.916666667 = -16.078151151

Reorder the terms:
-2.916666667 + x = -16.078151151

Solving
-2.916666667 + x = -16.078151151

Solving for variable 'x'.

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

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = -16.078151151 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = -16.078151151 + 2.916666667
x = -16.078151151 + 2.916666667

Combine like terms: -16.078151151 + 2.916666667 = -13.161484484
x = -13.161484484

Simplifying
x = -13.161484484


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.994817818, -13.161484484}

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