3x(x-6)=7

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Solution for 3x(x-6)=7 equation: 


Simplifying
3x(x + -6) = 7

Reorder the terms:
3x(-6 + x) = 7
(-6 * 3x + x * 3x) = 7
(-18x + 3x2) = 7

Solving
-18x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -18x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -18x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -6x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -6x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -6x + x2 = 0 + 2.333333333
-6x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-6x + x2 = 2.333333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 2.333333333 + 9

Reorder the terms:
9 + -6x + x2 = 2.333333333 + 9

Combine like terms: 2.333333333 + 9 = 11.333333333
9 + -6x + x2 = 11.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 11.333333333

Calculate the square root of the right side: 3.366501646

Break this problem into two subproblems by setting 
(x + -3) equal to 3.366501646 and -3.366501646.


Subproblem 1
x + -3 = 3.366501646

Simplifying
x + -3 = 3.366501646

Reorder the terms:
-3 + x = 3.366501646

Solving
-3 + x = 3.366501646

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.366501646 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.366501646 + 3
x = 3.366501646 + 3

Combine like terms: 3.366501646 + 3 = 6.366501646
x = 6.366501646

Simplifying
x = 6.366501646


Subproblem 2
x + -3 = -3.366501646

Simplifying
x + -3 = -3.366501646

Reorder the terms:
-3 + x = -3.366501646

Solving
-3 + x = -3.366501646

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.366501646 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.366501646 + 3
x = -3.366501646 + 3

Combine like terms: -3.366501646 + 3 = -0.366501646
x = -0.366501646

Simplifying
x = -0.366501646


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.366501646, -0.366501646}

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