Exercise 45 Page 379

Let's start by recalling how to solve equations that contain a variable that is squared and equal to a non-negative number. These types of equations have two solutions. x^2=a ⇒ x=± sqrt(a) This is because both (sqrt(a))^2 and (- sqrt(a))^2 are equal to a. Let's think of a more concrete example. sqrt(9)=±3 because 3^2=9 and (-3)^2=9 With this in mind, let's solve the given equation. 0.25r^2=49 First, we need to isolate the variable on one side of the equation. To do so, we will use the Multiplication Property of Equality.

0.25r^2=49

MultEqn

LHS * 4=RHS* 4

(0.25r^2)4=(49)4

CommutativePropMult

Commutative Property of Multiplication

0.25(4)r^2=(49)4

Multiply

Multiply

1r^2=196

IdPropMult

Identity Property of Multiplication

r^2=196

Next, since r is raised to the second power, we will take the square root of both sides. Let's do it!

r^2=196

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(r^2)=sqrt(196)

sqrt(a^2)=± a

r=± sqrt(196)

CalcRoot

Calculate root

r=± 14

The solutions are r=- 14 and r=14.