SOLUTION: one number is three less than twice another. the sum of their squares is 74. find the number

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Question 354682: one number is three less than twice another. the sum of their squares is 74. find the number
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
HI,
Let n be and (2n - 3) represent the numbers
.
questions states***
n%5E2+%2B+%282n-3%29%5E2+=+74
.
expand & simplify
n%5E2+%2B+4n%5E2+-12n+%2B+9+=+74
.
+5n%5E2+-12n++-+65+=+0
.
using quadratic formula to solve
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
n+=+%2812+%2B-+sqrt%28+1444+%29%29%2F%2810%29=+%2812+%2B-+38%29%2F%2810%29
.
n = -2.6 (does not qualify as the sum of the squares being 74 )
n = 5
*(2n - 3)= 7
.
check your answer
25 + 49 = 74