SOLUTION: the larger of two negative numbers is five more than the smaller. if the square of the larger number is increased by 27, the result is the smaller number multiplied by-7. find the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: the larger of two negative numbers is five more than the smaller. if the square of the larger number is increased by 27, the result is the smaller number multiplied by-7. find the       Log On


   

Question 266797: the larger of two negative numbers is five more than the smaller. if the square of the larger number is increased by 27, the result is the smaller number multiplied by-7. find the numbers
Found 2 solutions by drk, stanbon:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
From above we get the following:
(i) x+=+5+%2B+y
(ii) x%5E2+%2B+27+=+-7y
substitute (i) into (ii) to get
(iii) %285%2By%29%5E2+%2B+27+=+-7y
expand to get
(iv) y%5E2+%2B+10y+%2B+25+%2B+27+=+-7y
combine like terms and set = 0 to get
(v) y%5E2+%2B+17y+%2B+52+=+0
factoring, we get
(vi) %28y%2B13%29%28y%2B4%29+=+0
and solving for y, we get
y = -13 or y= -4
our two possible answers are:
(-8,-13) and (1,-4)
but we can't use the second.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the larger of two negative numbers is five more than the smaller. if the square of the larger number is increased by 27, the result is the smaller number multiplied by-7. find the numbers
---------------------
x-5 = y
----
x^2+27 = -7y
----------------------
Substitute for "y" and solve for "x".
x^2 + 27 = -7(x-5)
---
x^2 +27 = -7x + 35
---
x + 7x - 8 = 0
Factor:
(x+8)(x-1) = 0
Negative solution:
x = -8
---
since y = x-5
y = -13
==========================
Cheers,
Stan H.