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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 $$-1$$.
$$x-1=0$$ $$1$$ $$1$$ $$\Tblue{1}-1=0$$
$$x^2=1$$ $$2$$ $$-1$$, $$1$$ $$\Tblue{1}^2 = (\Tblue{-1})^2=1$$