SOLUTION: When solving for complementary angle if c= X 2 -4x+29 and D= 2x+13

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Question 1096421: When solving for complementary angle if c= X 2 -4x+29 and D= 2x+13
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

If angles C and D are complementary, then the sum of their measures is 90. So
%28x%5E2-4x%2B29%29+%2B+%282x%2B13%29+=+90
x%5E2-2x%2B42+=+90
x%5E2-2x-48+=+0
%28x-8%29%28x%2B6%29+=+0

x = 8 or x = -6

Now check to see if they both satisfy the original problem....

x = 8: C+=+x%5E2-4x%2B29+=+64-32%2B29+=+61 ; D+=+2x%2B13+=+16%2B13+=+29 ; 61+29 = 90 YES!

x = -6: C+=+x%5E2-4x%2B29+=+36%2B24%2B29+=+89 ; D+=+2x%2B13+=+-12%2B13+=+1 ; 89+1 = 90 YES!

There are two solutions to the problem:
(1) x = 8, making the two angles 61 and 29; and
(2) x = -6, making the two angles 89 and 1