Question

Solve for x if $4(2x+3{)}^2-(2x+3)-14=0$.

• A. c ≥ 4
• B. c ≤ 4
• C. $x=\frac{1}{2},-\frac{19}{8}$
• D. $x=-\frac{1}{2},\frac{19}{8}$

Answer 1

The correct option is A

c ≥ 4

Given: $4(2x+3{)}^2-(2x+3)-14=0$
Substitute $(2x+3)=y$, Hence the given equation reduces to
$4y^2-y-14=0$
$\Rightarrow$ $4y^2-8y+7y-14=0$
$\Rightarrow$ $4y(y-2)+7(y-2)=0$
$\Rightarrow$ $(4y+7)(y-2)=0$
$\Rightarrow$ $y=\frac{-7}{4}ory=2$
When $y=-\frac{7}{4}$,
$(2x+3)=-\frac{7}{4}$
$2x=-\frac{19}{4}$
$\Rightarrow$ $x=-\frac{19}{8}$
When $y=2$,
$(2x+3)=2$
$2x=-1$
$\Rightarrow$ $x=-\frac{1}{2}$