Exercise 64 Page 175

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

x=3/2 and x=1/4

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start by writing all the terms on one side of the equals sign. We will also factor out a GCF, if we find one.

- 32x^2+56x=12

SubEqn

LHS-12=RHS-12

- 32x^2+56x-12=0

FactorOut

Factor out - 4

- 4(8x^2-14x+3)=0

WriteDiff

Write as a difference

- 4(8x^2-2x-12x+3)=0

▼

Factor out 2x & - 3

FactorOut

Factor out 2x

- 4(2x(4x-1)-12x+3 )=0

FactorOut

Factor out - 3

- 4(2x(4x-1)-3(4x-1) )=0

FactorOut

Factor out (4x-1)

- 4(2x-3)(4x-1)=0

Solving

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

- 4(2x-3)(4x-1)=0

DivEqn

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

(2x-3)(4x-1)=0

ZeroProdProp

Use the Zero Product Property

lc2x-3=0 & (I) 4x-1=0 & (II)

▼

(I): Solve for x

AddEqn

(I): LHS+3=RHS+3

l2x=3 4x-1=0

DivEqn

(I): .LHS /2.=.RHS /2.

lx= 32 4x-1=0

▼

(I): Solve for x

AddEqn

(II): LHS+1=RHS+1

lx= 32 4x=1

DivEqn

(II): .LHS /4.=.RHS /4.

lx_1= 32 x_2= 14

Subchapter links

Exercises p.174-177

100

101

102

103

Exercise 64 Page 175

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Check the answer

Practice exercises

Asses your skill

Factoring

Solving