# The product of two consecutive numbers is 56. What are the numbers? Please show solution.

2
by CarlPaolo

2016-07-07T05:12:34+08:00
7x8
consecutive number ang 7at8 and ang product nila at 56
Thanks, Carlos. That is an easy guess. But how did you come up with that answer aside from guessing? What solution did you used?
• Brainly User
2016-07-07T09:10:02+08:00
First number: x
Second number: x+1

Equation:
(x) (x+1) = 56
x² + x - 56 = 0    ⇒   quadratic equation

Solve for x (roots) by factoring:
(x + 8) (x - 7) = 0

x + 8 = 0            x - 7 = 0
x = -8               x = 7

Check:
1) Plug-in -8
First number: x = -8
Second number: x +1 = -8 + 1 = -7
(-8) (-7) = 56

2) Plug-in 7:
First number: x = 7
Second number: x + 1 = 7 + 1 = 8
(7) (8) = 56

ANSWER: Since the problem does not specify that the two numbers are positive or negative number, the two numbers are -8 and -7,   or  7 and 8.
Thanks, momGie. But can you please show how did you factor that quadratic equation to come up with 7 and 8. Of course, by just looking at the problem, we can safely say 7 and 8 but how did we come up with that?
Given that the numerical coefficient(a) of of first term is 1, the factors of constant must be the sum of the numerical coefficient (b) of the middle term. The possible factors of -56 are (-8) and (7), or (-7) and (8) that could satisfy that statement. The sum of the first set of factors is -1, while the second set of factors is 1 (the coefficient, b, of middle term). So choose the second set of factors, (-7) and (8).
Factoring quadratic trinomial is a skill. But it is the easiest method to finding the roots, that is, if the equation can be factored. By knowing how to get the discriminant of the equation, one can choose what method to use. If you have doubts in what to use, quadratic formula (a tedious one) is the method applicable to all forms of quadratic equation.
Forgive my spontaneity. I hope I explained well :-) You may check my profile, and check similar problems I've solved involving quadratic equation. Have a great day :-)
Very much thanks, momGie. You are really great mathematician. I've tried solving similar problems following the pattern you've explained and it works. This helps me a lot in my assignments and improves my knowledge on this. Again, thank you momGie. Mabuhay po kayo.