r^2+5r=11

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Solution for r^2+5r=11 equation:


Simplifying
r2 + 5r = 11

Reorder the terms:
5r + r2 = 11

Solving
5r + r2 = 11

Solving for variable 'r'.

Reorder the terms:
-11 + 5r + r2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 5r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 5r + 11 + r2 = 0 + 11

Reorder the terms:
-11 + 11 + 5r + r2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 5r + r2 = 0 + 11
5r + r2 = 0 + 11

Combine like terms: 0 + 11 = 11
5r + r2 = 11

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = 11 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 11 + 6.25

Combine like terms: 11 + 6.25 = 17.25
6.25 + 5r + r2 = 17.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(r + 2.5) equal to 4.153311931 and -4.153311931.

Subproblem 1

r + 2.5 = 4.153311931 Simplifying r + 2.5 = 4.153311931 Reorder the terms: 2.5 + r = 4.153311931 Solving 2.5 + r = 4.153311931 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 4.153311931 + -2.5 r = 4.153311931 + -2.5 Combine like terms: 4.153311931 + -2.5 = 1.653311931 r = 1.653311931 Simplifying r = 1.653311931

Subproblem 2

r + 2.5 = -4.153311931 Simplifying r + 2.5 = -4.153311931 Reorder the terms: 2.5 + r = -4.153311931 Solving 2.5 + r = -4.153311931 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -4.153311931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -4.153311931 + -2.5 r = -4.153311931 + -2.5 Combine like terms: -4.153311931 + -2.5 = -6.653311931 r = -6.653311931 Simplifying r = -6.653311931

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.653311931, -6.653311931}

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