Exercise 14 Page 376

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. 7n^2=175 First, we need to isolate the variable term on one side of the equation. To do so, we will use the Division Property of Equality.

7n^2=175

DivEqn

.LHS /7.=.RHS /7.

7n^2/7=175/7

FactorOut

Factor out 7

7n^2/7=7(25)/7

CancelCommonFac

Cancel out common factors

7n^2/7=7(25)/7

SimpQuot

Simplify quotient

n^2/1=25/1

DivByOne

a/1=a

n^2=25

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

n^2=25

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(n^2)=sqrt(25)

sqrt(a^2)=± a

n=± sqrt(25)

CalcRoot

Calculate root

n=± 5

The solutions are n=- 5 and n=5.