(r-3)(r+17)=-20

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Solution for (r-3)(r+17)=-20 equation:


Simplifying
(r + -3)(r + 17) = -20

Reorder the terms:
(-3 + r)(r + 17) = -20

Reorder the terms:
(-3 + r)(17 + r) = -20

Multiply (-3 + r) * (17 + r)
(-3(17 + r) + r(17 + r)) = -20
((17 * -3 + r * -3) + r(17 + r)) = -20
((-51 + -3r) + r(17 + r)) = -20
(-51 + -3r + (17 * r + r * r)) = -20
(-51 + -3r + (17r + r2)) = -20

Combine like terms: -3r + 17r = 14r
(-51 + 14r + r2) = -20

Solving
-51 + 14r + r2 = -20

Solving for variable 'r'.

Reorder the terms:
-51 + 20 + 14r + r2 = -20 + 20

Combine like terms: -51 + 20 = -31
-31 + 14r + r2 = -20 + 20

Combine like terms: -20 + 20 = 0
-31 + 14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 14r + 31 + r2 = 0 + 31

Reorder the terms:
-31 + 31 + 14r + r2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 14r + r2 = 0 + 31
14r + r2 = 0 + 31

Combine like terms: 0 + 31 = 31
14r + r2 = 31

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 = 31 + 49

Reorder the terms:
49 + 14r + r2 = 31 + 49

Combine like terms: 31 + 49 = 80
49 + 14r + r2 = 80

Factor a perfect square on the left side:
(r + 7)(r + 7) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + 7) equal to 8.94427191 and -8.94427191.

Subproblem 1

r + 7 = 8.94427191 Simplifying r + 7 = 8.94427191 Reorder the terms: 7 + r = 8.94427191 Solving 7 + r = 8.94427191 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 = 8.94427191 + -7 Combine like terms: 7 + -7 = 0 0 + r = 8.94427191 + -7 r = 8.94427191 + -7 Combine like terms: 8.94427191 + -7 = 1.94427191 r = 1.94427191 Simplifying r = 1.94427191

Subproblem 2

r + 7 = -8.94427191 Simplifying r + 7 = -8.94427191 Reorder the terms: 7 + r = -8.94427191 Solving 7 + r = -8.94427191 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 = -8.94427191 + -7 Combine like terms: 7 + -7 = 0 0 + r = -8.94427191 + -7 r = -8.94427191 + -7 Combine like terms: -8.94427191 + -7 = -15.94427191 r = -15.94427191 Simplifying r = -15.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.94427191, -15.94427191}

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