Intermediate Algebra (11th edition)

The steps for solving a quadratic equation by factoring are summarized here.

SECTION 6.5 Solving Equations by Factoring 345

Solving a Quadratic Equation by Factoring

Step 1 Write in standard form.Rewrite the equation if necessary so that

one side is 0.

Step 2 Factorthe polynomial.

Step 3 Use the zero-factor property.Set each variable factor equal to 0.

Step 4 Find the solution(s).Solve each equation formed in Step 3.

Step 5 Checkeach solution in the originalequation.

Solving Quadratic Equations by Factoring

Solve each equation.

(a)

Step 1

Standard form

Step 2 Factor.

Step 3 or Zero-factor property

Step 4 or Solve each equation.

Step 5 Checkeach solution in the original equation.

x=

1

2

2 x= 1 x=- 2

2 x- 1 = 0 x + 2 = 0

12 x- 121 x+ 22 = 0

2 x^2 + 3 x- 2 = 0

2 x^2 + 3 x= 2

2 x^2 + 3 x= 2

EXAMPLE 2

Let

2 = 2 ✓ True

8 - 6  2

2142 - 6  2

x=-2.

21 - 222 + 31 - 22  2

CHECK 2 x^2 + 3 x= 2

Let

2 = 2 ✓ True

1

2

+

3

2

 2

2 a

1

4

b +

3

2

 2

2 a x=^12.

1

2

b

2

+ 3 a

1

2

b 2

2 x^2 + 3 x= 2

NOW TRY
EXERCISE 2
Solve each equation.

(a)

(b) 16 x^2 + 40 x+ 25 = 0

7 x= 3 - 6 x^2

NOW TRY ANSWERS

2. (a)E- 23 , 31 F (b)E- 45 F

Because both solutions check, the solution set is

(b) Standard form

Factor.

Zero-factor property

Add 1.

x= Divide by 2.

1

2

2 x= 1

2 x- 1 = 0

12 x- 122 = 0

4 x^2 - 4 x+ 1 = 0

E-2,

1

2 F.

We could factor as

12 x- 1212 x- 12.

There is only one solution, called a double solution,because the trinomial is a

perfect square. The solution set is E NOW TRY

1

2 F.