45-14r-r^2=0

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Solution for 45-14r-r^2=0 equation:


Simplifying
45 + -14r + -1r2 = 0

Solving
45 + -14r + -1r2 = 0

Solving for variable 'r'.

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

Divide each side by '-1'.
-45 + 14r + r2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 14r + 45 + r2 = 0 + 45

Reorder the terms:
-45 + 45 + 14r + r2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 14r + r2 = 0 + 45
14r + r2 = 0 + 45

Combine like terms: 0 + 45 = 45
14r + r2 = 45

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 = 45 + 49

Reorder the terms:
49 + 14r + r2 = 45 + 49

Combine like terms: 45 + 49 = 94
49 + 14r + r2 = 94

Factor a perfect square on the left side:
(r + 7)(r + 7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(r + 7) equal to 9.695359715 and -9.695359715.

Subproblem 1

r + 7 = 9.695359715 Simplifying r + 7 = 9.695359715 Reorder the terms: 7 + r = 9.695359715 Solving 7 + r = 9.695359715 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 = 9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + r = 9.695359715 + -7 r = 9.695359715 + -7 Combine like terms: 9.695359715 + -7 = 2.695359715 r = 2.695359715 Simplifying r = 2.695359715

Subproblem 2

r + 7 = -9.695359715 Simplifying r + 7 = -9.695359715 Reorder the terms: 7 + r = -9.695359715 Solving 7 + r = -9.695359715 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 = -9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + r = -9.695359715 + -7 r = -9.695359715 + -7 Combine like terms: -9.695359715 + -7 = -16.695359715 r = -16.695359715 Simplifying r = -16.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.695359715, -16.695359715}

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