Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 169975: I really need help solving the following problem. Any assistance you can provide me in doing so will be greatly appreciated. Thanks!
One number is 6 less than another. The product of the number is 72. Find the numbers.: I really need help solving the following problem. Any assistance you can provide me in doing so will be greatly appreciated. Thanks!
One number is 6 less than another. The product of the number is 72. Find the numbers.
Answer by jim_thompson5910(9911) About Me  (Show Source):
You can put this solution on YOUR website!
"One number is 6 less than another." translates to y=x-6


"The product of the number is 72" translates to x*y=72


x*y=72 Start with the second equation


x(x-6)=72 Plug in y=x-6


x^2-6x=72 Distribute.


x^2-6x-72=0 Subtract 72 from both sides.


Notice we have a quadratic equation in the form of ax^2+bx+c where a=1, b=-6, and c=-72


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(-6) +- sqrt( (-6)^2-4(1)(-72) ))/(2(1)) Plug in a=1, b=-6, and c=-72


x = (6 +- sqrt( (-6)^2-4(1)(-72) ))/(2(1)) Negate -6 to get 6.


x = (6 +- sqrt( 36-4(1)(-72) ))/(2(1)) Square -6 to get 36.


x = (6 +- sqrt( 36--288 ))/(2(1)) Multiply 4(1)(-72) to get -288


x = (6 +- sqrt( 36+288 ))/(2(1)) Rewrite sqrt(36--288) as sqrt(36+288)


x = (6 +- sqrt( 324 ))/(2(1)) Add 36 to 288 to get 324


x = (6 +- sqrt( 324 ))/(2) Multiply 2 and 1 to get 2.


x = (6 +- 18)/(2) Take the square root of 324 to get 18.


x = (6 + 18)/(2) or x = (6 - 18)/(2) Break up the expression.


x = (24)/(2) or x = (-12)/(2) Combine like terms.


x = 12 or x = -6 Simplify.


So the answers are x = 12 or x = -6


This means that the numbers are:


12 and 6

OR...

-6 and -12