(x)(x-6)=306

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Solution for (x)(x-6)=306 equation: 


Simplifying
(x)(x + -6) = 306

Reorder the terms:
x(-6 + x) = 306
(-6 * x + x * x) = 306
(-6x + x2) = 306

Solving
-6x + x2 = 306

Solving for variable 'x'.

Reorder the terms:
-306 + -6x + x2 = 306 + -306

Combine like terms: 306 + -306 = 0
-306 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '306' to each side of the equation.
-306 + -6x + 306 + x2 = 0 + 306

Reorder the terms:
-306 + 306 + -6x + x2 = 0 + 306

Combine like terms: -306 + 306 = 0
0 + -6x + x2 = 0 + 306
-6x + x2 = 0 + 306

Combine like terms: 0 + 306 = 306
-6x + x2 = 306

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 = 306 + 9

Reorder the terms:
9 + -6x + x2 = 306 + 9

Combine like terms: 306 + 9 = 315
9 + -6x + x2 = 315

Factor a perfect square on the left side:
(x + -3)(x + -3) = 315

Calculate the square root of the right side: 17.748239349

Break this problem into two subproblems by setting 
(x + -3) equal to 17.748239349 and -17.748239349.


Subproblem 1
x + -3 = 17.748239349

Simplifying
x + -3 = 17.748239349

Reorder the terms:
-3 + x = 17.748239349

Solving
-3 + x = 17.748239349

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 = 17.748239349 + 3

Combine like terms: -3 + 3 = 0
0 + x = 17.748239349 + 3
x = 17.748239349 + 3

Combine like terms: 17.748239349 + 3 = 20.748239349
x = 20.748239349

Simplifying
x = 20.748239349


Subproblem 2
x + -3 = -17.748239349

Simplifying
x + -3 = -17.748239349

Reorder the terms:
-3 + x = -17.748239349

Solving
-3 + x = -17.748239349

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 = -17.748239349 + 3

Combine like terms: -3 + 3 = 0
0 + x = -17.748239349 + 3
x = -17.748239349 + 3

Combine like terms: -17.748239349 + 3 = -14.748239349
x = -14.748239349

Simplifying
x = -14.748239349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.748239349, -14.748239349}

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