Question

The expression n2 + n represents the total number of blocks used in the nth figure of a pattern. Use the equation n2 + n = 56 to determine which figure has 56 blocks.

Answer 1

This is an equation that is quadratic in form. so to solve th given equation we must first factor it:
n2 + n = 56n2 + n - 56 = 0( n - 7 ) ( n + 8 ) = 0equate to zeron - 7 = 0n = 7andn + 8 = 0n = - 8
so the 7th figure has 56 blocks because there are no negative nth figure

Answer 2

We have to solve this quadratic equation $n^{2}+n=56$ for n to get which figure has 56 blocks.

$n^{2}+n=56\\n^{2}+n-56=0$

For middle term factorization, we need two numbers that multiplied gives us -56 and added gives us 1 (coefficient of n).

Such two numbers are 8 and -7. We can now write,

$n^{2}+n-56=0\\(n+8)(n-7)=0\\n=-8, 7$

"There is no negative figure number possible, so we disregard -8"

Our answer is 7.

ANSWER: The 7th figure has 56 blocks.