r^2=14r+40

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Solution for r^2=14r+40 equation:


Simplifying
r2 = 14r + 40

Reorder the terms:
r2 = 40 + 14r

Solving
r2 = 40 + 14r

Solving for variable 'r'.

Reorder the terms:
-40 + -14r + r2 = 40 + 14r + -40 + -14r

Reorder the terms:
-40 + -14r + r2 = 40 + -40 + 14r + -14r

Combine like terms: 40 + -40 = 0
-40 + -14r + r2 = 0 + 14r + -14r
-40 + -14r + r2 = 14r + -14r

Combine like terms: 14r + -14r = 0
-40 + -14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -14r + 40 + r2 = 0 + 40

Reorder the terms:
-40 + 40 + -14r + r2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -14r + r2 = 0 + 40
-14r + r2 = 0 + 40

Combine like terms: 0 + 40 = 40
-14r + r2 = 40

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 = 40 + 49

Reorder the terms:
49 + -14r + r2 = 40 + 49

Combine like terms: 40 + 49 = 89
49 + -14r + r2 = 89

Factor a perfect square on the left side:
(r + -7)(r + -7) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(r + -7) equal to 9.433981132 and -9.433981132.

Subproblem 1

r + -7 = 9.433981132 Simplifying r + -7 = 9.433981132 Reorder the terms: -7 + r = 9.433981132 Solving -7 + r = 9.433981132 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 = 9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + r = 9.433981132 + 7 r = 9.433981132 + 7 Combine like terms: 9.433981132 + 7 = 16.433981132 r = 16.433981132 Simplifying r = 16.433981132

Subproblem 2

r + -7 = -9.433981132 Simplifying r + -7 = -9.433981132 Reorder the terms: -7 + r = -9.433981132 Solving -7 + r = -9.433981132 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 = -9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + r = -9.433981132 + 7 r = -9.433981132 + 7 Combine like terms: -9.433981132 + 7 = -2.433981132 r = -2.433981132 Simplifying r = -2.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. r = {16.433981132, -2.433981132}

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