r^2+3r-5=11

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Solution for r^2+3r-5=11 equation:


Simplifying
r2 + 3r + -5 = 11

Reorder the terms:
-5 + 3r + r2 = 11

Solving
-5 + 3r + r2 = 11

Solving for variable 'r'.

Reorder the terms:
-5 + -11 + 3r + r2 = 11 + -11

Combine like terms: -5 + -11 = -16
-16 + 3r + r2 = 11 + -11

Combine like terms: 11 + -11 = 0
-16 + 3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + 3r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3r + r2 = 0 + 16
3r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
3r + r2 = 16

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 16 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3r + r2 = 18.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(r + 1.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

r + 1.5 = 4.272001873 Simplifying r + 1.5 = 4.272001873 Reorder the terms: 1.5 + r = 4.272001873 Solving 1.5 + r = 4.272001873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = 4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = 4.272001873 + -1.5 r = 4.272001873 + -1.5 Combine like terms: 4.272001873 + -1.5 = 2.772001873 r = 2.772001873 Simplifying r = 2.772001873

Subproblem 2

r + 1.5 = -4.272001873 Simplifying r + 1.5 = -4.272001873 Reorder the terms: 1.5 + r = -4.272001873 Solving 1.5 + r = -4.272001873 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + r = -4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + r = -4.272001873 + -1.5 r = -4.272001873 + -1.5 Combine like terms: -4.272001873 + -1.5 = -5.772001873 r = -5.772001873 Simplifying r = -5.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.772001873, -5.772001873}

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