Question

Consider the equation x(square) + 4px + 2q = 0 where p and q are real constants.

a) by completing square, show that (x+2p)square =4P(SQUARE)-2q

b) Hence show that x= -2p +/- square root(4 p(square) -2p )

c) Use the above results to solve the equations
1) x(square) + 8x +14 =0
2) x(square) -16x -6 =0

Answer 1

x^2 + 4px + 2q = 0
x^2 + 4px + (2p)^2 + 2q - (2p)^2 = 0
(x+2p)^2 = 4p^2 - 2q

b follows immediately
c and d just use part b to evaluate the roots.

Answer 2

Evaluate square root of 25+x square dx