r^2+10r=9

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Solution for r^2+10r=9 equation:


Simplifying
r2 + 10r = 9

Reorder the terms:
10r + r2 = 9

Solving
10r + r2 = 9

Solving for variable 'r'.

Reorder the terms:
-9 + 10r + r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 10r + 9 + r2 = 0 + 9

Reorder the terms:
-9 + 9 + 10r + r2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 10r + r2 = 0 + 9
10r + r2 = 0 + 9

Combine like terms: 0 + 9 = 9
10r + r2 = 9

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 = 9 + 25

Reorder the terms:
25 + 10r + r2 = 9 + 25

Combine like terms: 9 + 25 = 34
25 + 10r + r2 = 34

Factor a perfect square on the left side:
(r + 5)(r + 5) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(r + 5) equal to 5.830951895 and -5.830951895.

Subproblem 1

r + 5 = 5.830951895 Simplifying r + 5 = 5.830951895 Reorder the terms: 5 + r = 5.830951895 Solving 5 + r = 5.830951895 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 = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + r = 5.830951895 + -5 r = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 r = 0.830951895 Simplifying r = 0.830951895

Subproblem 2

r + 5 = -5.830951895 Simplifying r + 5 = -5.830951895 Reorder the terms: 5 + r = -5.830951895 Solving 5 + r = -5.830951895 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 = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + r = -5.830951895 + -5 r = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 r = -10.830951895 Simplifying r = -10.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.830951895, -10.830951895}

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