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.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Solving x^2+bx+c=0

Continue to next subchapter

Exercise 22 Page 49

Make sure you rewrite the equation leaving all the terms on one side. Then, solve by factoring.

- 3, 9

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.

x^2-6x=27

LHS-27=RHS-27

x^2-6x-27=0

Write as a difference

x^2+3x-9x-27=0

▼

Factor out x & - 9

Factor out x

x(x+3)-9x-27=0

Factor out - 9

x(x+3)-9(x+3)=0

Factor out (x+3)

(x+3)(x-9)=0

Solving

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

(x+3)(x-9)=0

Use the Zero Product Property

lcx+3=0 & (I) x-9=0 & (II)

(I): LHS-3=RHS-3

lx=- 3 x-9=0

(II): LHS+9=RHS+9

lx_1=- 3 x_2=9

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=- 3.

x^2-6x=27

x= - 3

( -3)^2-6( -3)? =27

▼

Simplify

Calculate power

9-6(-3)? =27

MultNegNegOnePar

- a(- b)=a* b

9+18? =27

Add terms

27=27 ✓

Substituting and simplifying created a true statement, so we know that x=- 3 is a solution of the equation. Let's move on to x=9.

x^2-6x=27

x= 9

9^2-6( 9)? =27

▼

Simplify

Calculate power

81-6(9)? =27

Multiply

81-54? =27

Subtract term

27=27 ✓

Again, we created a true statement. x=9 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51