If a number is added to it's square,the result is 42. How do you find the number?

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Answer 1 · 2016-01-07T16:51:19

There are two numbers which satisfy the criteria
#x=6,x=-7#

Let the number be #=x#, this number is added to its square #x^2#

#x+x^2=42#

Now, we solve the equation in order to find #x#

#x^2+x-42=0#

We first factorise the expression.

We can Split the Middle Term of this expression to factorise it.

#x^2+x-42=x^2+7x-6x-42#

#=x(x+7)-6(x+7)#
#=color(blue)((x-6)(x+7)#

Equating the factors to zero we get two values for #x#

#x=6,x=-7#