Solve the equation. (3x-4)^{2}-25=0

Dottie Parra 2021-09-29 Answered
Solve the equation. $$\displaystyle{\left({3}{x}-{4}\right)}^{{{2}}}-{25}={0}$$

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Step 1
We have to solve the equation:
$$\displaystyle{\left({3}{x}-{4}\right)}^{{{2}}}-{25}={0}$$
Solving this quadratic equation,
$$\displaystyle{\left({3}{x}-{4}\right)}^{{{2}}}-{25}={0}$$
$$\displaystyle{\left({3}{x}-{4}\right)}^{{{2}}}={25}$$
$$\displaystyle{\left({3}{x}-{4}\right)}=\pm\sqrt{{{25}}}$$
$$\displaystyle{\left({3}{x}-{4}\right)}=\pm{5}$$
$$\displaystyle{3}{x}={4}\pm{5}$$
$$\displaystyle{x}={\frac{{{4}\pm{5}}}{{{3}}}}$$
Step 2
Therefore,
$$\displaystyle{x}={\frac{{{4}\pm{5}}}{{{3}}}}$$
$$\displaystyle={\frac{{{4}+{5}}}{{{3}}}},{\frac{{{4}-{5}}}{{{3}}}}$$
$$\displaystyle={\frac{{{9}}}{{{3}}}},{\frac{{-{1}}}{{{3}}}}$$
$$\displaystyle={3},-{\frac{{{1}}}{{{3}}}}$$
Hence, solutions of the equation are $$\displaystyle{x}={3},-{\frac{{{1}}}{{{3}}}}$$.
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