Question

18. Solve the following equations by the method of completion of square

(ii) 7x
${}^{2}$
– 13x – 2=0
(iii) 15x² + 53x + 42 = 0​

Answer 1

Answer:

(1)

$7x {}^{2} - 13x - 2 = 0 \\ 7x {}^{2} - 14x + x - 2 = 0 \\ 7x(x - 2) + 1(x - 2) = 0 \\ (x - 2)(7x + 1) = 0 \\ s \: either \: \: \: (x - 2) = 0 = > x = 2 \\ or \: \: \: \: (7x + 1) = 0 = > x = \frac{ - 1}{7}$

(2)

$15 x{}^{2} + 53x + 42 = 0 \\ 15x {}^{2} + 35x + 18x + 42 = 0 \\ 5x(3x + 7) + 6(3x + 7) = 0 \\ (3x + 7)(5x + 6) = 0 \\ theefore \: \: \: ... \\ x = \frac{ - 7}{3} \: \: \: and \: x = \frac{ - 6}{5}$