How do you solve (x)(x+1)=56?

2 Answers
Aug 5, 2017

x = 7" " or " "x = -8

Explanation:

Given:

(x)(x+1) = 56

Here's one approach...

We want a pair of factors of 56 which differ by 1.

Note that 7*8 = 56, so one solution is x=7

The given equation is a quadratic (since if multiplied out it has term x^2 of degree 2), so will normally have two solutions. So what is the other?

The product of two negative numbers is positive, so we find the other solution given by:

(-8)(-7) = 56

That is: x=-8

Aug 5, 2017

x = 7 & -8

Explanation:

(x)(x+1) = 56

=> x²+x = 56

=> x²+x-56 = 0

=> Apply Quadratic Formula, x = (-b+-sqrt(b^2-4*a*c))/(2*a)

=> a = 1, b = 1, c = -56

=> x = (-1+-sqrt(1^2-(4*1*-56)))/(2*1)

=> x = (-1+-sqrt(1-(-224)))/2

=> x = (-1+-sqrt(1+224))/2

=> x = (-1+-sqrt225)/2

=> x = (-1+-15)/2

=> x = (-1+15)/2 & (-1-15)/2

=> x = 14/2 & -16/2

=> x = 7 & -8