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91Ó°ÊÓ

In the following exercise, solve the completing squares-

b2+6b=41

Short Answer

Expert verified

The required value of b is52-3,-52-3

Step by step solution

01

Step 1. Given information

The equation:b2+6b=41

02

Step 2. Calculation

Solving the equation,

b2+6b=41

⇒b2+6b+12×62=41+12×62

⇒b2+6b+9=41+9

localid="1645259869172" ⇒b2+6b+9=50

⇒b2+3b+3b+9=50

⇒b(b+3)+3(b+3)=50⇒(b+3)(b+3)=50

localid="1645270880664" ⇒(b+3)2=50⇒b+3=±52

localid="1645270913552" ⇒b=±52-3⇒b=52-3,-52-3

The required value of bis localid="1645270951341" 52-3,-52-3

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