Calculate: (x+1)^2-x^2=0

Expression: ${\left( x+1 \right)}^{2}-{x}^{2}=0$

Use ${\left( a+b \right)}^{2}={a}^{2}+2ab+{b}^{2}$ to expand the expression

${x}^{2}+2x+1-{x}^{2}=0$

Since two opposites add up to $0$, remove them from the expression

$2x+1=0$

Move the constant to the right-hand side and change its sign

$2x=-1$

Divide both sides of the equation by $2$

$\begin{align*}&x=-\frac{ 1 }{ 2 } \\&\begin{array} { l }x=-0.5,& x=-{2}^{-1}\end{array}\end{align*}$