(r+1)(r+1)+(r-8)(r-8)=45

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Solution for (r+1)(r+1)+(r-8)(r-8)=45 equation: 


Simplifying
(r + 1)(r + 1) + (r + -8)(r + -8) = 45

Reorder the terms:
(1 + r)(r + 1) + (r + -8)(r + -8) = 45

Reorder the terms:
(1 + r)(1 + r) + (r + -8)(r + -8) = 45

Multiply (1 + r) * (1 + r)
(1(1 + r) + r(1 + r)) + (r + -8)(r + -8) = 45
((1 * 1 + r * 1) + r(1 + r)) + (r + -8)(r + -8) = 45
((1 + 1r) + r(1 + r)) + (r + -8)(r + -8) = 45
(1 + 1r + (1 * r + r * r)) + (r + -8)(r + -8) = 45
(1 + 1r + (1r + r2)) + (r + -8)(r + -8) = 45

Combine like terms: 1r + 1r = 2r
(1 + 2r + r2) + (r + -8)(r + -8) = 45

Reorder the terms:
1 + 2r + r2 + (-8 + r)(r + -8) = 45

Reorder the terms:
1 + 2r + r2 + (-8 + r)(-8 + r) = 45

Multiply (-8 + r) * (-8 + r)
1 + 2r + r2 + (-8(-8 + r) + r(-8 + r)) = 45
1 + 2r + r2 + ((-8 * -8 + r * -8) + r(-8 + r)) = 45
1 + 2r + r2 + ((64 + -8r) + r(-8 + r)) = 45
1 + 2r + r2 + (64 + -8r + (-8 * r + r * r)) = 45
1 + 2r + r2 + (64 + -8r + (-8r + r2)) = 45

Combine like terms: -8r + -8r = -16r
1 + 2r + r2 + (64 + -16r + r2) = 45

Reorder the terms:
1 + 64 + 2r + -16r + r2 + r2 = 45

Combine like terms: 1 + 64 = 65
65 + 2r + -16r + r2 + r2 = 45

Combine like terms: 2r + -16r = -14r
65 + -14r + r2 + r2 = 45

Combine like terms: r2 + r2 = 2r2
65 + -14r + 2r2 = 45

Solving
65 + -14r + 2r2 = 45

Solving for variable 'r'.

Reorder the terms:
65 + -45 + -14r + 2r2 = 45 + -45

Combine like terms: 65 + -45 = 20
20 + -14r + 2r2 = 45 + -45

Combine like terms: 45 + -45 = 0
20 + -14r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7r + r2) = 0

Factor a trinomial.
2((2 + -1r)(5 + -1r)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2

Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {2, 5}

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