If we decided to try to calculate using the assumption that x is small, we get the following:

first Ka value

H3PO4

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H+

+

H2PO4–
Initial

0.100

0

0
Equilibrium

0.100–x

x

x

Ka1=        x2       = 6.9 x 10-3
             0.100

x = 0.026

0.026 is 26% of 0.100 (greater than 5%) and so the assumption is not good.

This is not the same as when we calculated using the quadratic. (0.023)

Proof that the assumption gives us the wrong answer.