SOLUTION: Find a number so that the square of the number is 28 more than three times the number. Thank you

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Question 292167: Find a number so that the square of the number is 28 more than three times the number. Thank you
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the required number, then:
n%5E2+=+3n%2B28 Rearrange into the standard form for a quadratic equation.
n%5E2-3n-28+=+0 Factor this quadratic equation.
%28n%2B4%29%28n-7%29+=+0 Apply the "zero product" rule.
n%2B4+=+0 or n-7+=+0 so that...
highlight%28n+=+-4%29 or highlight%28n+=+7%29
So there are two answers to this problem. Let's check them both:
n%5E2+=+3n%2B28 Substitute n = -4.
%28-4%29%5E2+=+3%28-4%29%2B28
16+=+-12%2B28
16+=+16 OK for n = -3.
n%5E2+=+3n%2B28 Substitute n = 7.
7%5E2+=+3%287%29%2B28
49+=+21%2B28
49+=+49 OK for n = 7.