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 $x$

$x=6,x=-7$