Answer
$\{2\}$.
Work Step by Step
Use FOIL method on the left side and special formula $(a+b)^2=a^2+2ab+b^2$ on the right side to obtain:
$x\cdot x- x\cdot 1+7\cdot x-7\cdot 1=x^2+2x+1$
Simplify.
$x^2- x+7 x-7=x^2+2x+1$
$x^2+6 x-7=x^2+2x+1$
Add $-x^2-2x+7$ to both sides.
$x^2+6 x-7-x^2-2x+7=x^2+2x+1-x^2-2x+7$
Simplify.
$4x=8$
Divide both sides by $4$.
$\dfrac{4x}{4}=\dfrac{8}{4}$
Simplify.
$x=2$
Hence, the solution to the equation is $\{2\}$.
