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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 45 Page 230

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.

- 4, 52

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+8x=5x+20

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Simplify

LHS-5x=RHS-5x

2x^2+3x=20

LHS-20=RHS-20

2x^2+3x-20=0

Write as a difference

2x^2+8x-5x-20=0

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Factor out 2x & - 5

Factor out 2x

2x(x+4)-5x-20=0

Factor out (- 5)

2x(x+4)-5(x+4)=0

Factor out (x+4)

(x+4)(2x-5)=0

Solving

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

(x+4)(2x-5)=0

Use the Zero Product Property

lcx+4=0 & (I) 2x-5=0 & (II)

(I): LHS-4=RHS-4

lx=- 4 2x-5=0

(II): LHS+5=RHS+5

lx=- 4 2x=5

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

lx_1=- 4 x_2= 52

Checking Our Answer

Checking our answer

We can substitute our solutions back into the given equation and simplify to check if our answers are correct. We will start with x=- 4.

2x^2+8x=5x+20

x= - 4

2( - 4)^2+8( - 4)? =5( - 4)+20

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Simplify

Calculate power

2(16)+8(- 4)? =5(- 4)+20

a(- b)=- a * b

2(16)-32? =- 20+20

Multiply

32-32? =- 20+20

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=- 4 is a solution of the equation. Let's move on to x= 52.

2x^2+8x=5x+20

x= 5/2

2( 5/2)^2+8( 5/2)? =5( 5/2)+20

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Simplify

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

2(25/4)+8(5/2)? =5(5/2)+20

MoveLeftFacToNum

a*b/c= a* b/c

2* 25/4+8* 5/2? =5* 5/2+20

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

25/2+4* 5? =5* 5/2+20

Multiply

25/2+20? =25/2+20

Calculate quotient

12.5+20? =12.5+20

Add terms

32.5=32.5 ✓

Again, we created a true statement. x= 52 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