Question

Use the substitution $y=2x+3$ to solve for $x$, if $4(2x+3{)}^2-(2x+3)-14=0$

Answer 1

Step : Solve for $x$
$4(2x+3{)}^2-(2x+3)-14=0$
Let $y=2x+3$
Put $2x+3=y$ in the given equation, $4y^2-y-14=0$
$\Rightarrow 4y^2-8y+7y-14=0$
$\Rightarrow 4y(y-2)+7(y-2)=0$
$\Rightarrow (y-2)(4y+7)=0$
$\Rightarrow y-2=0$ or $4y+7=0$
$y=2$ or $y=-\frac{7}{4}$
As $y=2x+3$
$2x+3=2$ or $2x+3=\frac{-7}{4}$
$x=-\frac{1}{2}$ or $x=-\frac{19}{8}$
$\therefore$ Hence, $x=(-\frac{1}{2})$ and $x=\frac{-19}{8}$.