Our equation is -4x∧2 +9y∧2 +32x- 64 =0, to write it in standard form we start by re-arranging it:
-4x∧2 + 32x + 9y∧2- 64= 0
taking 64 to the other side,
-4x∧2 + 32x + 9y∧2 = 64
simplifying,
-4(x∧2 + 8x) + 9 (y∧2 +0) = 64
we add the square of half the coefficient of x and
-4(x∧2 + 8x + 16) + 9 (y∧2 + 0) = 64
then we have
-4 (x + 4)∧2 + 9 (y+0)∧2 = 64 , by so doing we have written the equation in the standard form.