Solution for Quadratic Equation 5x² – 22x – 15 = 0

Problem Statement

Solve the following quadratic equation:

\[ (xi) \quad 5x^2 – 22x – 15 = 0 \]

Detailed Solution

Sol.

\[ 5x^2 – 22x – 15 = 0 \]
\[ \therefore 5x^2 – 25x + 3x – 15 = 0 \]
\[ \therefore 5x(x – 5) + 3(x – 5) = 0 \]
\[ \therefore (x – 5) (5x + 3) = 0 \]
\[ \therefore x – 5 = 0 \quad \text{or} \quad 5x + 3 = 0 \]
\[ \therefore x = 5 \quad \text{or} \quad 5x = –3 \]

\[ \therefore x = 5 \quad \text{or} \quad x = \frac{-3}{5} \]