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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

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Exercise 45 Page 174

The difference between the consecutive even numbers is 2. Begin by assuming x is one of the even numbers. With this, define the other one and write an equation that models the situation.

24, 26 or -26, -24

Practice makes perfect

The difference between the consecutive even numbers is 2. If we assume that x is one of the even numbers, the other one can be x+ 2. Given that the product of them is 624, let's write an equation that models the situation. x( x+ 2)=624Now we can solve the equation for x.

x(x+2)=624

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Simplify

Distribute x

x^2+2x=624

LHS-624=RHS-624

x^2+2x-624=0

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Factorize

Write as a sum

x^2-24x+26x-624=0

Factor out x

x(x-24)+26x-624=0

Factor out 26

x(x-24)+26(x-24)=0

Factor out (x-24)

(x-24)(x+26)=0

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Zero Property of Multiplication

lx-24=0 x+26=0

(I): LHS+24=RHS+24

lx=24 x+26=0

(II): LHS-26=RHS-26

lx=24 x=-26

Therefore, we can have two pairs of consecutive even numbers for our case. I:& 24 and 26 II:& -26 and -24

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Exercises p.174-177