Take half the coefficient of the first-degree term, 8 x, and square the result.
Desired constantWe add this constant, 16, to eachside of the equation and continue solving as shown.
Add 16 to each side.or Square root property
or Add
CHECK Original equation
Let.✓True
The check of the other solution is similar. The solution set is
E-^4 +^26 , -^4 -^26 F, or E-^4 ^26 F.
0 = 0
16 - 826 + 6 - 32 + 826 + 10 0
A-^4 +^26 B^2 +^8 A-^4 +^26 B +^10 ^0 x=-^4 +^26
x^2 + 8 x+ 10 = 0
x=- 4 + 26 x=- 4 - 26 - 4.
x+ 4 = 26 x+ 4 =- 26
1 x+ 422 = 6
x^2 + 8 x+ 16 =- 10 + 16
c
1
2
18 2d
2= 42 = 16
500 CHAPTER 9 Quadratic Equations, Inequalities, and Functions
Factor on the left.
Add on the right.This is a
key step.Remember the middle
termwhen squaring- 4 + 26.
Completing the SquareTo solve by completing the square, use these steps.
Step 1 Be sure the second-degree (squared) term has coefficient 1.If
the coefficient of the second-degree term is 1, proceed to Step 2.
If the coefficient of the second-degree term is not 1 but some other
nonzero number a, divide each side of the equation by a.
Step 2 Write the equation in correct formso that terms with variables are
on one side of the equals symbol and the constant is on the other side.
Step 3 Square half the coefficient of the first-degree (linear) term.
Step 4 Add the square to each side.
Step 5 Factor the perfect square trinomial.One side should now be a per-
fect square trinomial. Factor it as the square of a binomial. Simplify
the other side.
Step 6 Solve the equation.Apply the square root property to complete the
solution.ax^2 + bx+c= 01 aZ 02
Solving a Quadratic Equation by Completing the SquareSolve
Since the coefficient of the squared term is 1, begin with Step 2.
Step 2 Add 1 to each side.
Step 3 Take half the coefficient of the first-degree term and square the result.
c
1
2
15 2d
2= a
5
2
b
2=
25
4
x^2 + 5 x= 1
x^2 + 5 x- 1 = 0.
EXAMPLE 7 1 a 12NOW TRY
EXERCISE 6
Solve .x^2 + 6 x- 2 = 0
NOW TRY ANSWER
6.E- 3 211 F
NOW TRY