r^2+10r-27=0

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Solution for r^2+10r-27=0 equation:


Simplifying
r2 + 10r + -27 = 0

Reorder the terms:
-27 + 10r + r2 = 0

Solving
-27 + 10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 10r + 27 + r2 = 0 + 27

Reorder the terms:
-27 + 27 + 10r + r2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 10r + r2 = 0 + 27
10r + r2 = 0 + 27

Combine like terms: 0 + 27 = 27
10r + r2 = 27

The r term is 10r.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10r + 25 + r2 = 27 + 25

Reorder the terms:
25 + 10r + r2 = 27 + 25

Combine like terms: 27 + 25 = 52
25 + 10r + r2 = 52

Factor a perfect square on the left side:
(r + 5)(r + 5) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(r + 5) equal to 7.211102551 and -7.211102551.

Subproblem 1

r + 5 = 7.211102551 Simplifying r + 5 = 7.211102551 Reorder the terms: 5 + r = 7.211102551 Solving 5 + r = 7.211102551 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + r = 7.211102551 + -5 r = 7.211102551 + -5 Combine like terms: 7.211102551 + -5 = 2.211102551 r = 2.211102551 Simplifying r = 2.211102551

Subproblem 2

r + 5 = -7.211102551 Simplifying r + 5 = -7.211102551 Reorder the terms: 5 + r = -7.211102551 Solving 5 + r = -7.211102551 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + r = -7.211102551 + -5 r = -7.211102551 + -5 Combine like terms: -7.211102551 + -5 = -12.211102551 r = -12.211102551 Simplifying r = -12.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.211102551, -12.211102551}

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