Answer
$x=-1, 2$
Work Step by Step
$f(x)=x^2$ and $g(x)=x+2$
Since we are solving for all the values of $x$ when $f(x) = g(x)$, set the function $f(x)=x^2$ equal to $g(x)=x+2$ and we get the following equation:
$x^2=x+2$
Subtract $x+2$ from both sides of the equation so that all the terms are on the left side:
$x^2-(x+2)=x+2-(x+2)$
$x^2-x-2=0$
Then, factor the left side of the equation. To do this, we need to find two numbers that multiply to get -2 and add to get -1. Those numbers are 1 and -2.
$(x+1)(x-2)=0$
Next, you can see that the above equation holds true when $x+1=0$ or $x-2=0$. Solve for $x$ in each equation individually as shown below:
$x+1=0$
Subtract 1 from both sides.
$x+1-1=0-1$
$x=-1$
Now for the other equation:
$x-2=0$
Add 2 to both sides of the equation:
$x-2+2=0+2$
$x=2$
So, the final solution is $x=-1, 2$
