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  • Which constant must be added and subtracted to solve the quadratic equation9x^{2}+\frac{3}{4}x-\sqrt{2}=0 by the method of completing the square? (A)\frac{1}{8}\\ (B)\frac{1}{64}\\ (C)\frac{1}{4}\\ (D)\frac{9}{64}

Which constant must be added and subtracted to solve the quadratic equation9x^{2}+\frac{3}{4}x-\sqrt{2}=0  by the method of completing the square?

\\(A)\frac{1}{8}\\ (B)\frac{1}{64}\\ (C)\frac{1}{4}\\ (D)\frac{9}{64}

Answers (1)

Here the given quadratic equation is 

 9x^{2}+\frac{3}{4}x-\sqrt{2}=0
 \\(3)^{2}+\frac{1}{4}(3x)-\sqrt{2}=0\\ (3x)^{2}+2 \times \left ( \frac{1}{8} \right )\times(3x)-\sqrt{2}=0  

\text{[add and subtract}\left ( \frac{1}{8} \right )^{2}] 

\\(3x)^{2}+2 \times \left ( \frac{1}{8} \right )\times(3x)+\left ( \frac{1}{8} \right )^{2}-\left ( \frac{1}{8} \right )^{2}-\sqrt{2}=0\\ (3x)^{2}+2 \times \left ( \frac{1}{8} \right )\times(3x)+\left ( \frac{1}{8} \right )^{2}=\left ( \frac{1}{8} \right )^{2}+\sqrt{2}\\ \because a^{2}+b^{2}+2ab=(a+b)^{2}\\

So        

 \left (3x+ \frac{1}{8} \right )^{2}=\frac{1+64\times\sqrt{2}}{64} \text{ Hence}\left (\frac{1}{8} \right )^{2}=\frac{1}{64}  \text{ should be added and subtracted in the equation} 9x^{2}+\frac{3}{4}x-\sqrt{2}=0  

\text{ for solving by completing the square method. }

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