Solve: \((x – 7)(x – 9) = 195\)

Q.Solve: \((x – 7)(x – 9) = 195\)

\((x - 7)(x - 9) = 195\) Or, \(x^2 - 9x - 7x + 63 - 195 = 0\) Or, \(x^2 - 16x - 132 = 0\) Or, \(x^2 - (22 - 6)x - 132 = 0\) Or, \(x^2 - 22x + 6x - 132 = 0\) Or, \(x(x - 22) + 6(x - 22) = 0\) Or, \((x - 22)(x + 6) = 0\) That is, either \((x - 22) = 0 \Rightarrow x = 22\) Or, \((x + 6) = 0 \Rightarrow x = -6\) Therefore, \(x = 22\) and \(x = -6\) are the solutions of the quadratic equation \((x - 7)(x - 9) = 195\).

Marks \((x_i)\)	0–4	5–9	10–14	15–19	20–24	25–29	30–34	35–39
Frequency \((f_i)\)	4	5	7	8	7	5	6	3

Class Interval	Frequency \((f_i)\)	Class Midpoint \((x_i)\)	\(f_i x_i\)
0–10	4	5	20
10–20	6	15	90
20–30	10	25	250
30–40	6	35	210
40–50	4	45	180
Total	\(\sum{f_i} = 30\)		\(\sum{f_i x_i} = 750\)