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# Solution of an equation

A solution of an equation is a value for the unknown that satisfies the equation.

$\Tblue{-1}$ the a solution of the equation $\Tred{x} +1 =0$ because $$(\Tblue{-1}) + 1 = 0.$$ $\Tgreen{0}$ is not a solution because $$(\Tgreen{0}) + 1 = 1 \ne 0.$$

The solution is also called the root or the zero of the equation.

An equation can have one, several or no solution.

Equation Number of solutions Solutions Reason
$x^2=-1$ $0$ None $x^2$ is always positive and so no number can be squared to equal $-1$.
$x-1=0$ $1$ $1$ $\Tblue{1}-1=0$
$x^2=1$ $2$ $-1$, $1$ $\Tblue{1}^2 = (\Tblue{-1})^2=1$