3x(3x-18)=180

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Solution for 3x(3x-18)=180 equation:


Simplifying
3x(3x + -18) = 180

Reorder the terms:
3x(-18 + 3x) = 180
(-18 * 3x + 3x * 3x) = 180
(-54x + 9x2) = 180

Solving
-54x + 9x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -54x + 9x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -54x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-20 + -6x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-20 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -6x + x2 = 0

Solving
-20 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -6x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -6x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -6x + x2 = 0 + 20
-6x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-6x + x2 = 20

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 = 20 + 9

Reorder the terms:
9 + -6x + x2 = 20 + 9

Combine like terms: 20 + 9 = 29
9 + -6x + x2 = 29

Factor a perfect square on the left side:
(x + -3)(x + -3) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -3) equal to 5.385164807 and -5.385164807.


Subproblem 1
x + -3 = 5.385164807

Simplifying
x + -3 = 5.385164807

Reorder the terms:
-3 + x = 5.385164807

Solving
-3 + x = 5.385164807

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 = 5.385164807 + 3

Combine like terms: -3 + 3 = 0
0 + x = 5.385164807 + 3
x = 5.385164807 + 3

Combine like terms: 5.385164807 + 3 = 8.385164807
x = 8.385164807

Simplifying
x = 8.385164807


Subproblem 2
x + -3 = -5.385164807

Simplifying
x + -3 = -5.385164807

Reorder the terms:
-3 + x = -5.385164807

Solving
-3 + x = -5.385164807

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 = -5.385164807 + 3

Combine like terms: -3 + 3 = 0
0 + x = -5.385164807 + 3
x = -5.385164807 + 3

Combine like terms: -5.385164807 + 3 = -2.385164807
x = -2.385164807

Simplifying
x = -2.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.385164807, -2.385164807}
Solution
x = {8.385164807, -2.385164807}

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