body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

5. Quadratic Equations

Finish the assignment

Continue to next subchapter

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

▼

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

▼

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

▼

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

▼

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