Answer
$a=3.65,-1.65$
Work Step by Step
$4a^2-8a=24$
Rewrite the equation as:
$a^2-2a=6$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-2$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-2)^2}{4}=1$
To complete the square, add $1$ on both sides.
$a^2-2a+1=6+1$
$\implies (a-1)^2=7$
$\implies a-1=2.65$
and
$\implies a-1=-2.65$
or, $a=3.65,-1.65$
