r^2+14r+7=-r

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Solution for r^2+14r+7=-r equation:


Simplifying
r2 + 14r + 7 = -1r

Reorder the terms:
7 + 14r + r2 = -1r

Solving
7 + 14r + r2 = -1r

Solving for variable 'r'.

Reorder the terms:
7 + 14r + r + r2 = -1r + r

Combine like terms: 14r + r = 15r
7 + 15r + r2 = -1r + r

Combine like terms: -1r + r = 0
7 + 15r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 15r + -7 + r2 = 0 + -7

Reorder the terms:
7 + -7 + 15r + r2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 15r + r2 = 0 + -7
15r + r2 = 0 + -7

Combine like terms: 0 + -7 = -7
15r + r2 = -7

The r term is 15r.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15r + 56.25 + r2 = -7 + 56.25

Reorder the terms:
56.25 + 15r + r2 = -7 + 56.25

Combine like terms: -7 + 56.25 = 49.25
56.25 + 15r + r2 = 49.25

Factor a perfect square on the left side:
(r + 7.5)(r + 7.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(r + 7.5) equal to 7.017834424 and -7.017834424.

Subproblem 1

r + 7.5 = 7.017834424 Simplifying r + 7.5 = 7.017834424 Reorder the terms: 7.5 + r = 7.017834424 Solving 7.5 + r = 7.017834424 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = 7.017834424 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = 7.017834424 + -7.5 r = 7.017834424 + -7.5 Combine like terms: 7.017834424 + -7.5 = -0.482165576 r = -0.482165576 Simplifying r = -0.482165576

Subproblem 2

r + 7.5 = -7.017834424 Simplifying r + 7.5 = -7.017834424 Reorder the terms: 7.5 + r = -7.017834424 Solving 7.5 + r = -7.017834424 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + r = -7.017834424 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + r = -7.017834424 + -7.5 r = -7.017834424 + -7.5 Combine like terms: -7.017834424 + -7.5 = -14.517834424 r = -14.517834424 Simplifying r = -14.517834424

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.482165576, -14.517834424}

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