SOLUTION: Can you help me solve this problem. Our topic is about quadratic equations by completing the square. The product of two numbers is 10 less than 16 times the smaller.If twice th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can you help me solve this problem. Our topic is about quadratic equations by completing the square. The product of two numbers is 10 less than 16 times the smaller.If twice th      Log On


   

Question 374113: Can you help me solve this problem.
Our topic is about quadratic equations by completing the square.
The product of two numbers is 10 less than 16 times the smaller.If twice the smaller is 5 more than the larger number, find the two numbers.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"The product of two numbers is 10 less than 16 times the smaller" ___ S * L = 16S - 10

"twice the smaller is 5 more than the larger" ___ 2S = L + 5 ___ 2S - 5 = L

substituting ___ S(2S - 5) = 16S - 10 ___ 2S^2 - 21S + 10 = 0

2S^2 - 21S = -10 ___ S^2 - (21/2)S = -5

S^2 - (21/2)S + (-21/4)^2 = -5 + (-21/4)^2

(S - (21/4)^2 = (-80/16) + (441/16) = 361/16 = (±19/4)^2

S = (19/4) + (21/4) = 10 ___ or ___ S = (-19/4) + (21/4) = 1/2

substituting ___ 2(10) - 5 = L ___ L = 15 ___ or ___ L = 2(1/2) - 5 = -4


using the negative root causes the "larger" to be the "smaller" , and vice versa