Exercise 33 Page 547

To solve the proportion, we will start by using the Cross Products Property. Remember that we will need to treat 9x+6 and 20x+4 as single quantities in the cross multiplication process. From here, we will continue solving for x by using the Distributive Property and the Properties of Equality.

(9x+6)3x=18(20x+4)

Distr

Distribute 3x

27x^2+18x=18(20x+4)

Distr

Distribute 18

27x^2+18x=360x+72

SubEqn

LHS-360x=RHS-360x

27x^2-342x=72

SubEqn

LHS-72=RHS-72

27x^2-342x-72=0

DivEqn

.LHS /9.=.RHS /9.

3x^2-38x-8=0

We get a quadratic equation. Now, we can identify the values of a, b, and c. 3x^2-38x-8=0 ⇕ 3x^2+( - 38)x+( - 8)=0 We see that a= 3, b= - 38, and c= - 8. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( - 38)±sqrt(( - 38)^2-4( 3)( - 8))/2( 3)

▼

Solve for x

NegNeg

- (- a)=a

x=38±sqrt((- 38)^2-4(3)(- 8))/2(3)

CalcPow

Calculate power

x=38±sqrt(1444-4(3)(- 8))/2(3)

Multiply

Multiply

x=38±sqrt(1444-12(- 8))/6

MultNegNegOnePar

- a(- b)=a* b

x=38±sqrt(1444+96)/6

AddTerms

Add terms

x=38±sqrt(1540)/6

Rewrite

Rewrite 1540 as 4 * 385

x=38±sqrt(4 * 385)/6

RootProd

sqrt(a* b)=sqrt(a)*sqrt(b)

x=38 ± sqrt(4) * sqrt(385)/6

CalcRoot

Calculate root

x=38 ± 2sqrt(385)/6

FactorOut

Factor out 2

x=2(19 ± sqrt(385))/2 * 3

ReduceFrac

a/b=.a /2./.b /2.

x=19 ± sqrt(385)/3

The solutions for this equation are x= 19 ± sqrt(385)3. Let's separate them into the positive and negative cases, then round to the nearest tenth.

x=19 ± sqrt(385)/3
x_1=19 + sqrt(385)/3	x_2=19 - sqrt(385)/3
x_1 ≈ 12.9	x_2 ≈ - 0.2

Using the Quadratic Formula, we found that the solutions of the given equation, rounded to the nearest tenth, are x_1=12.9 and x_2=- 0.2.