Answer
$x= -1$
Work Step by Step
The given equation is
$x^{2}=-1-2x$
Step 1:
Write the equation in standard form.
$x^{2}+2x+1=0$
Step 2:
Graph the related function
$y= x^{2}+2x+1$
Step 3:
Find the $x$-intercept(s).
The only $x$-intercept is at the vertex $(-1, 0)$.
So the solution is $x=-1$.
Check the solution:
$(-1)^2=1$
$-1-2(-1)=1\checkmark$
