Question

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

Answer 1

`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`

Answer 2

`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`