Exercise 43 Page 174

Make sure you rewrite the equation leaving all the terms on one side, and that you factor out the GCF if it exists.

x=3/4 and x= 5

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start by factoring out a GCF, if we find one.

- 8x^2+46x-30=0

FactorOut

Factor out 2

2(- 4x^2+23x-15)=0

WriteSum

Write as a sum

2(- 4x^2+20x+3x-15)=0

▼

Factor out - 4x & 3

FactorOut

Factor out - 4x

2 ( - 4x(x-5)+3x-5 )=0

FactorOut

Factor out 3

2 ( - 4x(x-5)+3(x-5) )=0

FactorOut

Factor out (x-5)

2(- 4x+3)(x-5)=0

Solving

To solve this equation, we will apply the Zero Product Property.

2(- 4x+3)(x-5)=0

DivEqn

.LHS /2.=.RHS /2.

(- 4x+3)(x-5)=0

ZeroProdProp

Use the Zero Product Property

lc- 4x+3=0 & (I) x-5=0 & (II)

▼

Solve for x

SubEqn

(I): LHS-3=RHS-3

l- 4x=- 3 x-5=0

DivEqn

(I): .LHS /(- 4).=.RHS /(- 4).

lx= - 3- 4 x-5=0

ReduceFrac

(I): a/b=.a /(- 1)./.b /(- 1).

lx= 34 x-5=0

AddEqn

(II): LHS+5=RHS+5

lx_1= 34 x_2= 5

Subchapter links

Exercises p.174-177

100

101

102

103

Exercise 43 Page 174

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Factoring

Solving