r^2+14r=37

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Solution for r^2+14r=37 equation:


Simplifying
r2 + 14r = 37

Reorder the terms:
14r + r2 = 37

Solving
14r + r2 = 37

Solving for variable 'r'.

Reorder the terms:
-37 + 14r + r2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 14r + 37 + r2 = 0 + 37

Reorder the terms:
-37 + 37 + 14r + r2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 14r + r2 = 0 + 37
14r + r2 = 0 + 37

Combine like terms: 0 + 37 = 37
14r + r2 = 37

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 = 37 + 49

Reorder the terms:
49 + 14r + r2 = 37 + 49

Combine like terms: 37 + 49 = 86
49 + 14r + r2 = 86

Factor a perfect square on the left side:
(r + 7)(r + 7) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(r + 7) equal to 9.273618495 and -9.273618495.

Subproblem 1

r + 7 = 9.273618495 Simplifying r + 7 = 9.273618495 Reorder the terms: 7 + r = 9.273618495 Solving 7 + r = 9.273618495 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 = 9.273618495 + -7 Combine like terms: 7 + -7 = 0 0 + r = 9.273618495 + -7 r = 9.273618495 + -7 Combine like terms: 9.273618495 + -7 = 2.273618495 r = 2.273618495 Simplifying r = 2.273618495

Subproblem 2

r + 7 = -9.273618495 Simplifying r + 7 = -9.273618495 Reorder the terms: 7 + r = -9.273618495 Solving 7 + r = -9.273618495 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 = -9.273618495 + -7 Combine like terms: 7 + -7 = 0 0 + r = -9.273618495 + -7 r = -9.273618495 + -7 Combine like terms: -9.273618495 + -7 = -16.273618495 r = -16.273618495 Simplifying r = -16.273618495

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.273618495, -16.273618495}

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