9r^2-18r-27=-4

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Solution for 9r^2-18r-27=-4 equation:


Simplifying
9r2 + -18r + -27 = -4

Reorder the terms:
-27 + -18r + 9r2 = -4

Solving
-27 + -18r + 9r2 = -4

Solving for variable 'r'.

Reorder the terms:
-27 + 4 + -18r + 9r2 = -4 + 4

Combine like terms: -27 + 4 = -23
-23 + -18r + 9r2 = -4 + 4

Combine like terms: -4 + 4 = 0
-23 + -18r + 9r2 = 0

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

Divide each side by '9'.
-2.555555556 + -2r + r2 = 0

Move the constant term to the right:

Add '2.555555556' to each side of the equation.
-2.555555556 + -2r + 2.555555556 + r2 = 0 + 2.555555556

Reorder the terms:
-2.555555556 + 2.555555556 + -2r + r2 = 0 + 2.555555556

Combine like terms: -2.555555556 + 2.555555556 = 0.000000000
0.000000000 + -2r + r2 = 0 + 2.555555556
-2r + r2 = 0 + 2.555555556

Combine like terms: 0 + 2.555555556 = 2.555555556
-2r + r2 = 2.555555556

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 2.555555556 + 1

Reorder the terms:
1 + -2r + r2 = 2.555555556 + 1

Combine like terms: 2.555555556 + 1 = 3.555555556
1 + -2r + r2 = 3.555555556

Factor a perfect square on the left side:
(r + -1)(r + -1) = 3.555555556

Calculate the square root of the right side: 1.885618083

Break this problem into two subproblems by setting 
(r + -1) equal to 1.885618083 and -1.885618083.

Subproblem 1

r + -1 = 1.885618083 Simplifying r + -1 = 1.885618083 Reorder the terms: -1 + r = 1.885618083 Solving -1 + r = 1.885618083 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 1.885618083 + 1 Combine like terms: -1 + 1 = 0 0 + r = 1.885618083 + 1 r = 1.885618083 + 1 Combine like terms: 1.885618083 + 1 = 2.885618083 r = 2.885618083 Simplifying r = 2.885618083

Subproblem 2

r + -1 = -1.885618083 Simplifying r + -1 = -1.885618083 Reorder the terms: -1 + r = -1.885618083 Solving -1 + r = -1.885618083 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -1.885618083 + 1 Combine like terms: -1 + 1 = 0 0 + r = -1.885618083 + 1 r = -1.885618083 + 1 Combine like terms: -1.885618083 + 1 = -0.885618083 r = -0.885618083 Simplifying r = -0.885618083

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.885618083, -0.885618083}

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