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Chapter 7: Q66. (page 352)

Solve the equation $x^{2} + \frac{1}{3} x - \frac{35}{36} = 0$ by completing the squares.

Short Answer

Expert verified

The solution for the given equation is $x = - \frac{2}{3} 卤 \frac{\sqrt{17}}{2 \sqrt{3}}$ .

Step by step solution

01

Step 1. Write down the given information.

The given equation is $x^{2} + \frac{1}{3} x - \frac{35}{36} = 0$ .

02

Step 2. Apply square completion method.

The given equation $x^{2} + \frac{1}{3} x - \frac{35}{36} = 0$ with the help of completing the square method is solved as:

$\begin{matrix} x^{2} + \frac{1}{3} x 鈭� \frac{35}{36} = 0 .... (Given) \\ x^{2} + \frac{1}{3} x = \frac{35}{36} .... (Rewrite) \\ x^{2} + \frac{1}{3} x + \frac{4}{9} = \frac{35}{36} + \frac{4}{9} .... (\begin{array}{l} Add {(\frac{2}{3})}^{2} \\ bothsides \end{array}) \\ {(x + \frac{2}{3})}^{2} = \frac{17}{12} \\ x + \frac{2}{3} = 卤 \frac{\sqrt{17}}{2 \sqrt{3}} \\ x = 鈭� \frac{2}{3} 卤 \frac{\sqrt{17}}{2 \sqrt{3}} \end{matrix}$

03

Step 3. Conclusion.

The solution for the given equation is $x = - \frac{2}{3} 卤 \frac{\sqrt{17}}{2 \sqrt{3}}$ .

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