# Solve the radical equation and check all proposed solutions. x-\sqrt{3x-2}

Solve the radical equation and check all proposed solutions.
$$\displaystyle{x}-\sqrt{{{3}{x}-{2}}}={4}$$

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SoosteethicU
Given equation is
$$\displaystyle{x}-\sqrt{{{3}{x}-{2}}}={4}$$
Rearranging the terms
$$\displaystyle{x}-{4}=\sqrt{{{3}{x}-{2}}}$$
Squaring both side
$$\displaystyle{\left({x}-{4}\right)}^{{2}}={\left(\sqrt{{{3}{x}-{2}}}\right)}^{{2}}$$
$$\displaystyle\Rightarrow{x}^{{2}}-{2}\times{4}\times{x}+{4}^{{2}}={3}{x}-{2}$$
$$\displaystyle\Rightarrow{x}^{{2}}-{8}{x}+{16}={3}{x}-{2}$$
$$\displaystyle\Rightarrow{x}^{{2}}-{11}{x}+{18}={0}$$
$$\displaystyle{x}^{{2}}-{11}{x}+{18}={0}$$
$$\displaystyle{x}^{{2}}-{9}{x}-{2}{x}+{18}={0}$$
$$\displaystyle{x}{\left({x}-{9}\right)}-{2}{\left({x}-{9}\right)}={0}$$
$$\displaystyle{\left({x}-{2}\right)}{\left({x}-{9}\right)}={0}$$
Hence, x=2,9