r^2-9r-38=-9

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Solution for r^2-9r-38=-9 equation:


Simplifying
r2 + -9r + -38 = -9

Reorder the terms:
-38 + -9r + r2 = -9

Solving
-38 + -9r + r2 = -9

Solving for variable 'r'.

Reorder the terms:
-38 + 9 + -9r + r2 = -9 + 9

Combine like terms: -38 + 9 = -29
-29 + -9r + r2 = -9 + 9

Combine like terms: -9 + 9 = 0
-29 + -9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -9r + 29 + r2 = 0 + 29

Reorder the terms:
-29 + 29 + -9r + r2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -9r + r2 = 0 + 29
-9r + r2 = 0 + 29

Combine like terms: 0 + 29 = 29
-9r + r2 = 29

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = 29 + 20.25

Reorder the terms:
20.25 + -9r + r2 = 29 + 20.25

Combine like terms: 29 + 20.25 = 49.25
20.25 + -9r + r2 = 49.25

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(r + -4.5) equal to 7.017834424 and -7.017834424.

Subproblem 1

r + -4.5 = 7.017834424 Simplifying r + -4.5 = 7.017834424 Reorder the terms: -4.5 + r = 7.017834424 Solving -4.5 + r = 7.017834424 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 7.017834424 + 4.5 r = 7.017834424 + 4.5 Combine like terms: 7.017834424 + 4.5 = 11.517834424 r = 11.517834424 Simplifying r = 11.517834424

Subproblem 2

r + -4.5 = -7.017834424 Simplifying r + -4.5 = -7.017834424 Reorder the terms: -4.5 + r = -7.017834424 Solving -4.5 + r = -7.017834424 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -7.017834424 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -7.017834424 + 4.5 r = -7.017834424 + 4.5 Combine like terms: -7.017834424 + 4.5 = -2.517834424 r = -2.517834424 Simplifying r = -2.517834424

Solution

The solution to the problem is based on the solutions from the subproblems. r = {11.517834424, -2.517834424}

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