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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

5. Quadratic Equations

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Exercise 11 Page 229

Make sure you rewrite the equation leaving all the terms on one side and that you factor out the greatest common factor if it exists.

- 1, 32

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.

2x^2-x=3

LHS-3=RHS-3

2x^2-x-3=0

Write as a difference

2x^2+2x-3x-3=0

▼

Factor out 2x & - 3

Factor out 2x

2x(x+1)-3x-3=0

Factor out (- 3)

2x(x+1)-3(x+1)=0

Factor out (x+1)

(x+1)(2x-3)=0

Solving

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

(x+1)(2x-3)=0

Use the Zero Product Property

lcx+1=0 & (I) 2x-3=0 & (II)

(I): LHS-1=RHS-1

lx=- 1 2x-3=0

(II): LHS+3=RHS+3

lx=- 1 2x=3

(II): .LHS /2.=.RHS /2.

lx_1=- 1 x_2= 32

Checking

We can substitute our solutions back into the given equation and simplify to check if our answers are correct. We will start with x=- 1.

2x^2-x=3

x= - 1

2( - 1)^2-( - 1)? =3

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Evaluate left-hand side

Calculate power

2(1)-(- 1)? =3

Identity Property of Multiplication

2-(- 1)? =3

- (- a)=a

2+1? =3

Add terms

3=3 ✓

Substituting and simplifying created a true statement, so we know that x=- 1 is a solution of the equation. Let's move on to x= 32.

2x^2-x=3

x= 3/2

2( 3/2)^2- 3/2? =3

▼

Evaluate left-hand side

(a/b)^m=a^m/b^m

2(9/4)-3/2? =3

MoveLeftFacToNum

a*b/c= a* b/c

2* 9/4-3/2? =3

a/b=.a /2./.b /2.

9/2-3/2? =3

Subtract fractions

6/2? =3

Calculate quotient

3=3 ✓

Again, we created a true statement. x= 32 is indeed a solution of the equation.

Subchapter links

Lesson Check p.229

Practice and Problem-Solving Exercises p.229-231

Standardized Test Prep p.231

Mixed Review p.231