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

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Don't Memorise
Jan 7, 2016

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

Explanation:

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#

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