Exercise 74 Page 347

Practice makes perfect

a To solve for w we will perform inverse operations until w is isolated. Notice that when you take the square root of an equation we get two solutions, one positive and one negative.

5w^2=17

DivEqn

.LHS /5.=.RHS /5.

w^2=17/5

SqrtEqn

sqrt(LHS)=sqrt(RHS)

w=± sqrt(17/5)

b This is a quadratic equation. We can solve for x by using the Quadratic Formula.

5w^2-3w-17=0

UseQuadForm

Use the Quadratic Formula: a = 5, b= - 3, c= - 17

w=-( - 3) ± sqrt(( - 3)^2-4( 5)( - 17))/2( 5)

NegNeg

- (- a)=a

w=3 ± sqrt((- 3)^2-4(5)(- 17))/2(5)

NegBaseToPosBase

(- a)^2=a^2

w=3 ± sqrt(3^2-4(5)(- 17))/2(5)

CalcPowProd

Calculate power and product

w=3 ± sqrt(9+340)/10

AddTerms

Add terms

w=3 ± sqrt(349)/10

StateSol

State solutions

w_1= 3+sqrt(349)10 w_2= 3 - sqrt(349)10

c Let's start by isolating the squared variable by dividing both sides by 2.

2w^2=-6

DivEqn

.LHS /2.=.RHS /2.

w^2=-3

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(w^2) = sqrt(-3)

CalcRoot

Calculate root

w = ± sqrt(-3)

▼

Simplify right-hand side

SplitIntoFactors

Split into factors

w = ± sqrt((-1)*3)

SqrtProd

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

w = ± sqrt(-1)sqrt(3)

SqrtNegOneToI

sqrt(- 1)= i

w = ± isqrt(3)

Subchapter links

6.2.1 At Your Service p.340

6.2.2 Angles on a Pool Table p.343-344

6.2.3 Shortest Distance Problems p.347-348

6.2.4 The Number System and Deriving the Quadratic Formula p.353

6.2.5 The Number System and Deriving the Quadratic Formula p.355-356

6.2.6 Analyzing a Game p.359-360

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Exercise 74 Page 347

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