+817 How do you solve this?
Find all values of $a$ such that $\frac{a-3}{\sqrt{a}} = -a \sqrt{a}$.
+129847 (a - 3) / √a = -a√a multiply both sides by √a
a - 3 = -a √a * √a simplify
a - 3 = -a * a
a - 3 = -a^2 add a^2 to both sides
a^2 + a - 3 = 0 complete the square on a ......(you could also use the Q Formula)
a^2 + a = 3
a^2 + a + 1/4 = 3 + 1/4
(a + 1/2)^2 = 13/4
(a cannot be negative because we can't have a negative under a radical - take the positive root )
a + 1/2 = sqrt (13) / 2
a = sqrt (13) / 2 - 1/2
a = [ sqrt (13) - 1 ] / 2
