Question 225116
One number is 2 more than 5 times another. Their product is 3. Find the numbers.


Step 1.  Let x be one number


Step 2.  Let 2+5x be the other number since its 2 more than 5 times the first number.


Step 3.  Then, {{{x(2+5x)=3}}} since their product is 3.


Step 4.  Turn this equation into a quadratic one in standard form as follows:


{{{x(2+5x)=3}}} 


{{{2x+5x^2=3}}}


Subtract 3 from both sides


{{{2x+5x^2-3=3-3}}}


Simplify and arrange in descending order to get our quadratic equation


{{{5x^2+2x-3=0}}}


Step 4.  To solve, use the quadratic formula given as 


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=5, b=2, and c=-3


*[invoke quadratic "x", 5, 2, -3 ]


With x=0.6 then 2+5x=2+5*0.6=5


With x=-1 then 2+5*(-1)=-3.


Step 5.  ANSWER:  The numbers are 0.6 and 5 as one pair and -1 and -3 as the other pair of numbers.


I hope the above steps and explanation were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV