r^2+2r-19=0

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Solution for r^2+2r-19=0 equation:


Simplifying
r2 + 2r + -19 = 0

Reorder the terms:
-19 + 2r + r2 = 0

Solving
-19 + 2r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 2r + 19 + r2 = 0 + 19

Reorder the terms:
-19 + 19 + 2r + r2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2r + r2 = 0 + 19
2r + r2 = 0 + 19

Combine like terms: 0 + 19 = 19
2r + r2 = 19

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 19 + 1

Reorder the terms:
1 + 2r + r2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + 2r + r2 = 20

Factor a perfect square on the left side:
(r + 1)(r + 1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(r + 1) equal to 4.472135955 and -4.472135955.

Subproblem 1

r + 1 = 4.472135955 Simplifying r + 1 = 4.472135955 Reorder the terms: 1 + r = 4.472135955 Solving 1 + r = 4.472135955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + r = 4.472135955 + -1 r = 4.472135955 + -1 Combine like terms: 4.472135955 + -1 = 3.472135955 r = 3.472135955 Simplifying r = 3.472135955

Subproblem 2

r + 1 = -4.472135955 Simplifying r + 1 = -4.472135955 Reorder the terms: 1 + r = -4.472135955 Solving 1 + r = -4.472135955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + r = -4.472135955 + -1 r = -4.472135955 + -1 Combine like terms: -4.472135955 + -1 = -5.472135955 r = -5.472135955 Simplifying r = -5.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.472135955, -5.472135955}

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