(r-2)(r+18)=25

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Solution for (r-2)(r+18)=25 equation:


Simplifying
(r + -2)(r + 18) = 25

Reorder the terms:
(-2 + r)(r + 18) = 25

Reorder the terms:
(-2 + r)(18 + r) = 25

Multiply (-2 + r) * (18 + r)
(-2(18 + r) + r(18 + r)) = 25
((18 * -2 + r * -2) + r(18 + r)) = 25
((-36 + -2r) + r(18 + r)) = 25
(-36 + -2r + (18 * r + r * r)) = 25
(-36 + -2r + (18r + r2)) = 25

Combine like terms: -2r + 18r = 16r
(-36 + 16r + r2) = 25

Solving
-36 + 16r + r2 = 25

Solving for variable 'r'.

Reorder the terms:
-36 + -25 + 16r + r2 = 25 + -25

Combine like terms: -36 + -25 = -61
-61 + 16r + r2 = 25 + -25

Combine like terms: 25 + -25 = 0
-61 + 16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 16r + 61 + r2 = 0 + 61

Reorder the terms:
-61 + 61 + 16r + r2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 16r + r2 = 0 + 61
16r + r2 = 0 + 61

Combine like terms: 0 + 61 = 61
16r + r2 = 61

The r term is 16r.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16r + 64 + r2 = 61 + 64

Reorder the terms:
64 + 16r + r2 = 61 + 64

Combine like terms: 61 + 64 = 125
64 + 16r + r2 = 125

Factor a perfect square on the left side:
(r + 8)(r + 8) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(r + 8) equal to 11.180339887 and -11.180339887.

Subproblem 1

r + 8 = 11.180339887 Simplifying r + 8 = 11.180339887 Reorder the terms: 8 + r = 11.180339887 Solving 8 + r = 11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + r = 11.180339887 + -8 r = 11.180339887 + -8 Combine like terms: 11.180339887 + -8 = 3.180339887 r = 3.180339887 Simplifying r = 3.180339887

Subproblem 2

r + 8 = -11.180339887 Simplifying r + 8 = -11.180339887 Reorder the terms: 8 + r = -11.180339887 Solving 8 + r = -11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -11.180339887 + -8 Combine like terms: 8 + -8 = 0 0 + r = -11.180339887 + -8 r = -11.180339887 + -8 Combine like terms: -11.180339887 + -8 = -19.180339887 r = -19.180339887 Simplifying r = -19.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.180339887, -19.180339887}

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