0=r^2+14r-219.8

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Solution for 0=r^2+14r-219.8 equation:


Simplifying
0 = r2 + 14r + -219.8

Reorder the terms:
0 = -219.8 + 14r + r2

Solving
0 = -219.8 + 14r + r2

Solving for variable 'r'.

Combine like terms: 0 + 219.8 = 219.8
219.8 + -14r + -1r2 = -219.8 + 14r + r2 + 219.8 + -14r + -1r2

Reorder the terms:
219.8 + -14r + -1r2 = -219.8 + 219.8 + 14r + -14r + r2 + -1r2

Combine like terms: -219.8 + 219.8 = 0.0
219.8 + -14r + -1r2 = 0.0 + 14r + -14r + r2 + -1r2
219.8 + -14r + -1r2 = 14r + -14r + r2 + -1r2

Combine like terms: 14r + -14r = 0
219.8 + -14r + -1r2 = 0 + r2 + -1r2
219.8 + -14r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
219.8 + -14r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-219.8 + 14r + r2 = 0

Move the constant term to the right:

Add '219.8' to each side of the equation.
-219.8 + 14r + 219.8 + r2 = 0 + 219.8

Reorder the terms:
-219.8 + 219.8 + 14r + r2 = 0 + 219.8

Combine like terms: -219.8 + 219.8 = 0.0
0.0 + 14r + r2 = 0 + 219.8
14r + r2 = 0 + 219.8

Combine like terms: 0 + 219.8 = 219.8
14r + r2 = 219.8

The r term is 14r.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14r + 49 + r2 = 219.8 + 49

Reorder the terms:
49 + 14r + r2 = 219.8 + 49

Combine like terms: 219.8 + 49 = 268.8
49 + 14r + r2 = 268.8

Factor a perfect square on the left side:
(r + 7)(r + 7) = 268.8

Calculate the square root of the right side: 16.395121226

Break this problem into two subproblems by setting 
(r + 7) equal to 16.395121226 and -16.395121226.

Subproblem 1

r + 7 = 16.395121226 Simplifying r + 7 = 16.395121226 Reorder the terms: 7 + r = 16.395121226 Solving 7 + r = 16.395121226 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 16.395121226 + -7 Combine like terms: 7 + -7 = 0 0 + r = 16.395121226 + -7 r = 16.395121226 + -7 Combine like terms: 16.395121226 + -7 = 9.395121226 r = 9.395121226 Simplifying r = 9.395121226

Subproblem 2

r + 7 = -16.395121226 Simplifying r + 7 = -16.395121226 Reorder the terms: 7 + r = -16.395121226 Solving 7 + r = -16.395121226 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -16.395121226 + -7 Combine like terms: 7 + -7 = 0 0 + r = -16.395121226 + -7 r = -16.395121226 + -7 Combine like terms: -16.395121226 + -7 = -23.395121226 r = -23.395121226 Simplifying r = -23.395121226

Solution

The solution to the problem is based on the solutions from the subproblems. r = {9.395121226, -23.395121226}

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