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

2
by CarlPaolo

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by CarlPaolo

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7x8

consecutive number ang 7at8 and ang product nila at 56

consecutive number ang 7at8 and ang product nila at 56

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**₁** = -8 ** ** x**₂** = 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.**

Second number: x+1

(x) (x+1) = 56

x² + x - 56 = 0 ⇒ quadratic equation

(x + 8) (x - 7) = 0

x + 8 = 0 x - 7 = 0

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

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.