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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 13 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.

- 2, - 1

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.

2x^2+6x=- 4
AddEqn

LHS+4=RHS+4

2x^2+6x+4=0
â–¼
.LHS /2.=.RHS /2.
FactorOut

Factor out 2

2(x^2+3x+2)=0
DivEqn

.LHS /2.=.RHS /2.

x^2+3x+2=0
WriteSum

Write as a sum

x^2+x+2x+2=0
â–¼
Factor out x & 2
FactorOut

Factor out x

x(x+1)+2x+2=0
FactorOut

Factor out 2

x(x+1)+2(x+1)=0
FactorOut

Factor out (x+1)

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

Solving

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

(x+2)(x+1)=0
ZeroProdProp

Use the Zero Product Property

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

(I): LHS-2=RHS-2

lx=- 2 x+1=0
SubEqn

(II): LHS-1=RHS-1

lx_1=- 2 x_2=- 1

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=- 2.

2x^2+6x=- 4
Substitute

x= - 2

2( - 2)^2+6( - 2)? =- 4
â–¼
Evaluate left-hand side
CalcPow

Calculate power

2(4)+6(- 2)? =- 4
MultPosNeg

a(- b)=- a * b

2(4)-12? =- 4
Multiply

Multiply

8-12? =- 4
SubTerm

Subtract term

- 4=- 4 ✓

Substituting and simplifying created a true statement, so we know that x=- 2 is a solution of the equation. Let's move on to x=- 1.

2x^2+6x=- 4
Substitute

x= - 1

2( - 1)^2+6( - 1)? =- 4
â–¼
Evaluate left-hand side
CalcPow

Calculate power

2(1)+6(- 1)? =- 4
IdPropMult

Identity Property of Multiplication

2+6(- 1)? =- 4
MultPosNeg

a(- b)=- a * b

2-6? =- 4
SubTerm

Subtract term

- 4=- 4 ✓

Again, we created a true statement. x=- 1 is indeed a solution of the equation.

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arrow_right Lesson Check p.229
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Lesson Check 4 (Page 229)
Lesson Check 5 (Page 229)
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arrow_right Practice and Problem-Solving Exercises p.229-231
Practice and Problem-Solving Exercises 9 (Page 229)
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Practice and Problem-Solving Exercises 13 (Page 229)
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arrow_right Standardized Test Prep p.231
Standardized Test Prep 60 (Page 231)
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