Exercise 41 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. x^2=100 Since x is raised to the second power, we will take the square root of both sides. Let's do it!

x^2=100

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(100)

sqrt(a^2)=± a

x=± sqrt(100)

CalcRoot

Calculate root

x=± 10

The solutions are x=- 10 and x=10.