Solve the following equation by factorization1 7 (3 x-5)^2=28 - Vidyadip

Question

Solve the following equation by factorization$\frac{1}{7}(3 x-5)^2=28$

✓

Answer

$
\begin{aligned}
& \frac{1}{7}(3 x-5)^2=28 \\
& (3 x-5)^2=28 \times 7 \\
& \Rightarrow 9 x^2-30 x+25=196 \\
& \Rightarrow 9 x^2-30 x+25-196=0 \\
& \Rightarrow 9 x^2-30 x-171=0 \\
& \Rightarrow 3 x^2-10 x-57=0 \\
& \Rightarrow 3 x^2-19 x+9 x-57=0 \\
& \Rightarrow x(3 x-19)+3(3 x-19)=0 \\
& \Rightarrow(3 x-19)(x+3)=0
\end{aligned}
$
Either $3 x-19=0$,
then $3 x=19$
$
\Rightarrow x =\frac{19}{3}
$
or
$
x+3=0 \text {, }
$
then $x=-3$
Hence $x=\frac{19}{3},-3$.

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