To do this, we group the $x$ terms and the $y$ terms together and complete the square for each.
\[\begin{aligned}
4x^2 - 32x + 9y^2 + 36y &= -64 \\
4(x^2 - 8x) + 9(y^2 + 4y) &= -64 \\
4[(x^2 - 8x + 16) - 16] + 9[(y^2 + 4y + 4) - 4] &= -64 \\
4[(x - 4)^2 - 16] +
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