r^2+12r-19=0

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Solution for r^2+12r-19=0 equation:


Simplifying
r2 + 12r + -19 = 0

Reorder the terms:
-19 + 12r + r2 = 0

Solving
-19 + 12r + 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 + 12r + 19 + r2 = 0 + 19

Reorder the terms:
-19 + 19 + 12r + r2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 12r + r2 = 0 + 19
12r + r2 = 0 + 19

Combine like terms: 0 + 19 = 19
12r + r2 = 19

The r term is 12r.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12r + 36 + r2 = 19 + 36

Reorder the terms:
36 + 12r + r2 = 19 + 36

Combine like terms: 19 + 36 = 55
36 + 12r + r2 = 55

Factor a perfect square on the left side:
(r + 6)(r + 6) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(r + 6) equal to 7.416198487 and -7.416198487.

Subproblem 1

r + 6 = 7.416198487 Simplifying r + 6 = 7.416198487 Reorder the terms: 6 + r = 7.416198487 Solving 6 + r = 7.416198487 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + r = 7.416198487 + -6 r = 7.416198487 + -6 Combine like terms: 7.416198487 + -6 = 1.416198487 r = 1.416198487 Simplifying r = 1.416198487

Subproblem 2

r + 6 = -7.416198487 Simplifying r + 6 = -7.416198487 Reorder the terms: 6 + r = -7.416198487 Solving 6 + r = -7.416198487 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + r = -7.416198487 + -6 r = -7.416198487 + -6 Combine like terms: -7.416198487 + -6 = -13.416198487 r = -13.416198487 Simplifying r = -13.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.416198487, -13.416198487}

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