Where's the problem in this equation? Resulting in $4 = 5$

Question

I just saw this equation and I can't find out where's the problem:

$$25-45 = 16-36$$

$$25- 2 \cdot 5 \cdot \frac{9}{2} = 16- 2\cdot4\cdot\frac{9}{2}$$

$$25 - 2\cdot 5\cdot \frac{9}{2} + \frac{81}{4} = 16 - 2\cdot 4 \cdot \frac{9}{2} + \frac{81}{4}$$

$$\left( 5-\frac{9}{2} \right) ^2 = \left (4-\frac{9}{2} \right) ^2$$

$$5-\frac{9}{2} = 4 - \frac{9}{2}$$ $$5=4$$

Answer 1

$a^2 = b^2$ does not imply that $a = b$.

Answer 2

$5-9/2$ is positive, $4-9/2$ is negative. They are not equal, although their squares are equal.