3x(3x)=(4x-4+5)9

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Solution for 3x(3x)=(4x-4+5)9 equation: 


Simplifying
3x(3x) = (4x + -4 + 5) * 9

Remove parenthesis around (3x)
3x * 3x = (4x + -4 + 5) * 9

Reorder the terms for easier multiplication:
3 * 3x * x = (4x + -4 + 5) * 9

Multiply 3 * 3
9x * x = (4x + -4 + 5) * 9

Multiply x * x
9x2 = (4x + -4 + 5) * 9

Reorder the terms:
9x2 = (-4 + 5 + 4x) * 9

Combine like terms: -4 + 5 = 1
9x2 = (1 + 4x) * 9

Reorder the terms for easier multiplication:
9x2 = 9(1 + 4x)
9x2 = (1 * 9 + 4x * 9)
9x2 = (9 + 36x)

Solving
9x2 = 9 + 36x

Solving for variable 'x'.

Reorder the terms:
-9 + -36x + 9x2 = 9 + 36x + -9 + -36x

Reorder the terms:
-9 + -36x + 9x2 = 9 + -9 + 36x + -36x

Combine like terms: 9 + -9 = 0
-9 + -36x + 9x2 = 0 + 36x + -36x
-9 + -36x + 9x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-9 + -36x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-1 + -4x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-1 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -4x + x2 = 0

Solving
-1 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x + x2 = 0 + 1
-4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4x + x2 = 1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + -4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4x + x2 = 5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -2 = 2.236067978

Simplifying
x + -2 = 2.236067978

Reorder the terms:
-2 + x = 2.236067978

Solving
-2 + x = 2.236067978

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.236067978 + 2
x = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
x = 4.236067978

Simplifying
x = 4.236067978


Subproblem 2
x + -2 = -2.236067978

Simplifying
x + -2 = -2.236067978

Reorder the terms:
-2 + x = -2.236067978

Solving
-2 + x = -2.236067978

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.236067978 + 2
x = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
x = -0.236067978

Simplifying
x = -0.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.236067978, -0.236067978}
Solution
x = {4.236067978, -0.236067978}

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