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

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.

${x}^{2} + x - 42 = {x}^{2} + 7 x - 6 x - 42$

$= x \left(x + 7\right) - 6 \left(x + 7\right)$
=color(blue)((x-6)(x+7)

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

$x = 6 , x = - 7$