Question

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

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

Answer 1

The correct option is C $x=-\frac{1}{2},-\frac{19}{8}$

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 $y=-\frac{7}{4}$,
$\Rightarrow (2x+3)=-\frac{7}{4}$
$\Rightarrow 2x=-\frac{19}{4}$
$\Rightarrow$ $x=-\frac{19}{8}$

When $y=2$,
$\Rightarrow (2x+3)=2$
$\Rightarrow 2x=-1$
$\Rightarrow$ $x=-\frac{1}{2}$