Chapter 10: Q 94 (page 1181)

Solve by completing the square:
$3 q^{2} - 5 q = 9$ .

Short Answer

Expert verified

The values of $q$ for the equation $3 q^{2} - 5 q = 9$ by completing the square are $\frac{5 + \sqrt{133}}{6}, \frac{5 - \sqrt{133}}{6}$ .

Step by step solution

Step 1. Given Information.

The equation is,

$3 q^{2} - 5 q = 9$ .

Step 2. Completing the square.

Given, $3 q^{2} - 5 q = 9$

Dividing both sides by $3$ to remove the coefficient of $q^{2}$ on both sides,

$\Rightarrow \frac{3 q^{2} - 5 q}{3} = \frac{9}{3} \Rightarrow q^{2} - \frac{5}{3} q = 3$

Adding the square to the half of $(- \frac{5}{3})$ on both sides,

$\Rightarrow q^{2} - \frac{5}{3} q + {(\frac{1}{2} (- \frac{5}{3}))}^{2} = 3 + {(\frac{1}{2} (- \frac{5}{3}))}^{2} \Rightarrow q^{2} - \frac{5}{3} q + \frac{25}{36} = 3 + \frac{25}{36} \Rightarrow q^{2} - \frac{5}{3} q + \frac{25}{36} = \frac{133}{36}$

Taking the left side as the binomial square,

$\Rightarrow {(q - \frac{5}{6})}^{2} = \frac{133}{36}$

Taking the square root on both sides,

$\Rightarrow q - \frac{5}{6} = \sqrt{\frac{133}{36}} \Rightarrow q - \frac{5}{6} = \pm \frac{\sqrt{133}}{6}$

Solving for the value of $q$ ,

$\Rightarrow q = \frac{5}{6} \pm \frac{\sqrt{133}}{6} \Rightarrow q = \frac{5}{6} + \frac{\sqrt{133}}{6} o r, q = \frac{5}{6} - \frac{\sqrt{133}}{6} \Rightarrow q = \frac{5 + \sqrt{133}}{6}, \frac{5 - \sqrt{133}}{6}$

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Solve by completing the square:
$3 q^{2} - 5 q = 9$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square.

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Solve by completing the square:3q2-5q=9.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Completing the square.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Decision Maths

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Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve by completing the square:
$3 q^{2} - 5 q = 9$ .