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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 51 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

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.

16x^2+36=- 48x

LHS+48x=RHS+48x

16x^2 + 48x+36=0

Factor out 4

4(4x^2+12x+9)=0

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

Write as a power

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

a^m* b^m=(a * b)^m

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

SplitIntoFactors

Split into factors

4((2x)^2+2 * 2x * 3 +3^2 )=0

FacPosPerfectSquare

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

4(2x+3)^2=0

Solving

To solve this equation, we will perform Inverse Operations on both sides of equation until the variable is isolated.

4(2x+3)^2=0

.LHS /4.=.RHS /4.

(2x+3)^2=0

sqrt(LHS)=sqrt(RHS)

2x+3=0

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Solve for x

LHS-3=RHS-3

2x=- 3

.LHS /2.=.RHS /2.

x=- 3/2

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 3/2

Subchapter links

Exercises p.174-177