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Question

# Which constant must be added and subtracted to solve the quadratic equation 9x2+34x−2=0 by the method of completing the square?

A

18

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B

164

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C

14

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D

964

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Solution

## The correct option is B 164 Given equation is 9x2+34x−2=0 ⇒(3x)2+14(3x)−2=0 On putting 3x = y, we have y2+14y−2=0 ⇒y2+14y+(18)2−(18)2−2=0⇒(y+18)2=164+2⇒(y+18)2=12964 ⇒y=±√1298−18 ⇒y=√129−18 or −(√129+1)8 Thus, (18)2=164 must be added and subtracted to solve the given equation.

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