Question

the square of a number is 20 more than 8times the number.find the number

Answer 1

Given:

Let the number be x.

According to the statement, we have:

$x^2=20+8x$

Simplifying it for x,

$x^2-8x-20=0$

Consider two terms such that their product is - 20 and their sum is -8

The terms will be - 10 and 2 since their product is -20 and their sum is -8 so we can write the equation as:

$x^2-10x+2x-20=0$

Now, take x common from first two terms and 2 from last two terms,

$x(x-10)+2(x-10)=0$

Now, take (x-10) common :

$(x-10)(x+2)=0$

Since the product of two terms is zero, so one must be zero or both must be zero.Hence,

$\begin{gathered} (x-10)(x+2)=0 \\ x=10,-2 \end{gathered}$

Hence, the number can be 10 or - 2.