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 $x = - \frac{2}{3} \pm \frac{\sqrt{17}}{2 \sqrt{3}}$ .

Step by step solution

Step 1. Write down the given information.

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

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:

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

Step 3. Conclusion.

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

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Apply square completion method.

Step 3. Conclusion.

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Solve the equation x2+13x-3536=0 by completing the squares.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Apply square completion method.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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