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Question
Solve the following quadratic equation by factorisation.
\[25 m^2 = 9\]
Solution
\[25 m^2 = 9\]
\[\Rightarrow 25 m^2 - 9 = 0\]
\[ \Rightarrow \left( 5m \right)^2 - 3^2 = 0\]
\[ \Rightarrow \left( 5m - 3 \right)\left( 5m + 3 \right) = 0 \left[ \because \left( x - a \right)\left( x + a \right) = x^2 - a^2 \right]\]
\[ \Rightarrow \left( 5m - 3 \right) = 0 \text{ or }\left( 5m + 3 \right) = 0\]
\[ \Rightarrow m = \frac{3}{5}, \frac{- 3}{5}\]
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