Chapter 9: Q.428. (page 983)

Solve by completing the square.
$5 q^{2} + 70 q + 20 = 0$

Short Answer

Expert verified

The required solution is $q = \pm 3 \sqrt{5} - 7$ .

Step by step solution

Step 1. Given information.

The given equation is $5 q^{2} + 70 q + 20 = 0$ .

Step 2. Isolate the variable and constant terms on one side.

$5 q^{2} + 70 q + 20 = 0 5 q^{2} + 70 q + 20 - 20 = 0 - 20 \dots \dots (s u b t r a c t i n g 20 f r o m b o t h s i d e s) 5 q^{2} + 70 q = - 20$

Step 3. Simplify the equation.

$\begin{array}{rcl} 5 q^{2} + 70 q & = & - 20 \\ \frac{5 q^{2}}{5} + \frac{70 q}{5} & = & - \frac{20}{5} \dots \dots (d i v i d e b o t h s i d e s b y 5) \\ q^{2} + 14 q & = & - 4 \\ q^{2} + 2 \cdot q \cdot 7 & = & - 4 \\ q^{2} + 2 \cdot q \cdot 7 + 7^{2} & = & - 4 + 7^{2} \dots \dots \dots (a d d b o t h s i d e s b y 7^{2}) \\ {(q + 7)}^{2} & = & - 4 + 49 \\ {(q + 7)}^{2} & = & 45 \\ q + 7 & = & \pm \sqrt{45} \\ q + 7 & = & \pm 3 \sqrt{5} \\ q & = & \pm 3 \sqrt{5} - 7 \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $q = \pm 3 \sqrt{5} - 7$ .

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Solve by completing the square.
$5 q^{2} + 70 q + 20 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Isolate the variable and constant terms on one side.

Step 3. Simplify the equation.

Step 4. Simplified answer.

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Solve by completing the square.5q2+70q+20=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Isolate the variable and constant terms on one side.

Step 3. Simplify the equation.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Logic and Functions

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$5 q^{2} + 70 q + 20 = 0$