9x^2-27x=20

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Solution for 9x^2-27x=20 equation:


Simplifying
9x2 + -27x = 20

Reorder the terms:
-27x + 9x2 = 20

Solving
-27x + 9x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -27x + 9x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -27x + 9x2 = 0

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

Divide each side by '9'.
-2.222222222 + -3x + x2 = 0

Move the constant term to the right:

Add '2.222222222' to each side of the equation.
-2.222222222 + -3x + 2.222222222 + x2 = 0 + 2.222222222

Reorder the terms:
-2.222222222 + 2.222222222 + -3x + x2 = 0 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + -3x + x2 = 0 + 2.222222222
-3x + x2 = 0 + 2.222222222

Combine like terms: 0 + 2.222222222 = 2.222222222
-3x + x2 = 2.222222222

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2.222222222 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2.222222222 + 2.25

Combine like terms: 2.222222222 + 2.25 = 4.472222222
2.25 + -3x + x2 = 4.472222222

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.472222222

Calculate the square root of the right side: 2.114762923

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.114762923 and -2.114762923.

Subproblem 1

x + -1.5 = 2.114762923 Simplifying x + -1.5 = 2.114762923 Reorder the terms: -1.5 + x = 2.114762923 Solving -1.5 + x = 2.114762923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.114762923 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.114762923 + 1.5 x = 2.114762923 + 1.5 Combine like terms: 2.114762923 + 1.5 = 3.614762923 x = 3.614762923 Simplifying x = 3.614762923

Subproblem 2

x + -1.5 = -2.114762923 Simplifying x + -1.5 = -2.114762923 Reorder the terms: -1.5 + x = -2.114762923 Solving -1.5 + x = -2.114762923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.114762923 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.114762923 + 1.5 x = -2.114762923 + 1.5 Combine like terms: -2.114762923 + 1.5 = -0.614762923 x = -0.614762923 Simplifying x = -0.614762923

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.614762923, -0.614762923}

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