Exercise 54 Page 175

Make sure you rewrite the equation leaving all the terms on one side.

x=- 3/4 and x= 2/5

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.

- 7x +6 = 20x^2

SubEqn

LHS-20x^2=RHS-20x^2

- 20x^2-7x+6=0

WriteDiff

Write as a difference

- 20x^2+8x-15x+6=0

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Factor out - 4x & - 3

FactorOut

Factor out - 4x

- 4x(5x-2)-15x+6=0

FactorOut

Factor out - 3

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

FactorOut

Factor out (5x-2)

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

Solving

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

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

ZeroProdProp

Use the Zero Product Property

lc- 4x-3=0 & (I) 5x-2=0 & (II)

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(I): Solve for x

AddEqn

(I): LHS+3=RHS+3

l- 4x=3 5x-2=0

DivEqn

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

lx= 3- 4 5x-2=0

MoveNegDenomToFrac

(I): Put minus sign in front of fraction

lx=- 34 5x-2=0

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(II): Solve for x

AddEqn

(II): LHS+2=RHS+2

lx=- 34 5x=2

DivEqn

(II): .LHS /5.=.RHS /5.

lx_1=- 34 x_2= 25

Subchapter links

Exercises p.174-177

100

101

102

103

Exercise 54 Page 175

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Factoring

Solving