r^2+16r=-19

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Solution for r^2+16r=-19 equation:


Simplifying
r2 + 16r = -19

Reorder the terms:
16r + r2 = -19

Solving
16r + r2 = -19

Solving for variable 'r'.

Reorder the terms:
19 + 16r + r2 = -19 + 19

Combine like terms: -19 + 19 = 0
19 + 16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 16r + -19 + r2 = 0 + -19

Reorder the terms:
19 + -19 + 16r + r2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 16r + r2 = 0 + -19
16r + r2 = 0 + -19

Combine like terms: 0 + -19 = -19
16r + r2 = -19

The r term is 16r.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16r + 64 + r2 = -19 + 64

Reorder the terms:
64 + 16r + r2 = -19 + 64

Combine like terms: -19 + 64 = 45
64 + 16r + r2 = 45

Factor a perfect square on the left side:
(r + 8)(r + 8) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(r + 8) equal to 6.708203933 and -6.708203933.

Subproblem 1

r + 8 = 6.708203933 Simplifying r + 8 = 6.708203933 Reorder the terms: 8 + r = 6.708203933 Solving 8 + r = 6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 6.708203933 + -8 Combine like terms: 8 + -8 = 0 0 + r = 6.708203933 + -8 r = 6.708203933 + -8 Combine like terms: 6.708203933 + -8 = -1.291796067 r = -1.291796067 Simplifying r = -1.291796067

Subproblem 2

r + 8 = -6.708203933 Simplifying r + 8 = -6.708203933 Reorder the terms: 8 + r = -6.708203933 Solving 8 + r = -6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -6.708203933 + -8 Combine like terms: 8 + -8 = 0 0 + r = -6.708203933 + -8 r = -6.708203933 + -8 Combine like terms: -6.708203933 + -8 = -14.708203933 r = -14.708203933 Simplifying r = -14.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-1.291796067, -14.708203933}

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