Question

2(y+2)square-11(y+2)-21=0

Answer 1

We have

$2(y + 2) {}^{2} - 11(y + 2) - 21 = 0$

We will expand (y+2)² using the following identity

$\boxed {( {a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab }$

Now,

=> 2 (y² + 4 +2(y)(2) ) -11y - 22 -21 = 0

=> 2(y² +4 +4y) -11y -43 = 0

=> 2y² +8 +8y -11y -43 = 0

=> 2y² -3y -35 = 0

Now we will use middle term splitting method

=> 2y² -10y + 7y -35 = 0

=> 2y(y-5) +7(y-5) = 0

=> (2y+7) (y-5) = 0

=> 2y+7 = 0 or y-5 = 0

$</strong><strong> </strong><strong> </strong><strong>= > y = \frac{ - 7}{ \: \: 2} \: \: or \: \: y = 5</strong><strong>$