Factoring Quadratics

Since the equation is already written in factored form, we will use the Zero Product Property to solve it.

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

ZeroProdPropUse the Zero Product Property

2 - 4 x = 0 2 + 4 x = 0 (I) (II)

(I):

LHS - 2 = RHS - 2

- 4 x = - 2 2 + 4 x = 0

(I):

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

x = \frac{- 2}{- 4} 2 + 4 x = 0

(I):

\frac{a}{b} = \frac{a / ( - 2 )}{b / ( - 2 )}

x = \frac{1}{2} 2 + 4 x = 0

(II):

LHS - 2 = RHS - 2

x = \frac{1}{2} 4 x = - 2

(II):

LHS / 4 = RHS / 4

x = \frac{1}{2} x = \frac{- 2}{4}

(II):

Put minus sign in front of fraction

x = \frac{1}{2} x = - \frac{2}{4}

(II):

\frac{a}{b} = \frac{a / 2}{b / 2}

x = \frac{1}{2} x = - \frac{1}{2}

We found that the solutions of the equation are

x = - \frac{1}{2}

and

x = \frac{1}{2} .

Factoring Quadratics 1.13 - Solution