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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Expert Answer

Layton
Answered 2021-09-30 Author has 8199 answers
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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