The complete solution of the equation √p + √q = 2x will be 

1
\(z = \frac{1}{6}{\left( {2x - a} \right)^3} + {a^2}y + b\), where a and b are arbitrary constants.
2
\(z = \frac{1}{3}{\left( {a + 2x} \right)^3} + {a^2}y + b\), where a and b are arbitrary constants.
3
\(z = \frac{1}{4}{\left( {a + 2x} \right)^2} + {a^2}y + b\), where a and b are arbitrary constants.
4
\(z = \frac{1}{4}{\left( {2x - a} \right)^2} + {a^2}y + b\), where a and b are arbitrary constants.

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