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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 15 Page 174

Recall the formula a^2± 2ab+b^2=(a± b)^2.

6

Practice makes perfect

To solve the given equation by factoring, we will have to factor a perfect square trinomial. a^2± 2ab+b^2 ⇔ (a± b)^2

Factoring

Before we begin, let's rewrite the equation with all the non-zero terms on the left-hand side. 2x^2-24x=- 72 ⇔ 2x^2-24x+72=0 Since it appears that the expression on the left-hand side has a GCF, let's factor that out. 2x^2-24x+72=0 ⇔ 2(x^2-12x+36)=0 Now that all the terms are on the left-hand side and there is no GCF to factor out, let's start factoring.

2(x^2-12x+36)=0

.LHS /2.=.RHS /2.

x^2-12x+36=0

FacNegPerfectSquare

a^2-2ab+b^2=(a-b)^2

(x-6)^2=0

SplitIntoFactors

Split into factors

(x-6)(x-6)=0

Solving

Now let's apply the Zero Product Property to solve.

(x-6)(x-6)=0

Use the Zero Product Property

lcx-6=0 & (I) x-6=0 & (II)

(I), (II): LHS+6=RHS+6

lx_1=6 x_2=6

The only solution to this equation is x=6.

Subchapter links

Exercises p.174-177