Exercise 64 Page 139

We want to solve the quadratic equation by completing the square. Note that all terms with x are on one side of the equation. x^2 - 9x = - 12 In a quadratic expression, b is the linear coefficient. For the equation above, we have that b=- 9. Let's now calculate ( b2 )^2.

( b/2 )^2

Substitute

b= - 9

( - 9/2 )^2

▼

Simplify

MoveNegNumToFrac

Put minus sign in front of fraction

(- 9/2)^2

NegBaseToPosBase

(- a)^2=a^2

(9/2)^2

PowQuot

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

9^2/2^2

CalcPow

Calculate power

81/4

Next, we will add ( b2 )^2= 814 to both sides of our equation. Then, we will factor the trinomial on the left-hand side, and solve the equation.

x^2 - 9x = - 12

AddEqn

LHS+81/4=RHS+81/4

x^2- 9x + 81/4=- 12+ 81/4

FacNegPerfectSquare

a^2-2ab+b^2=(a-b)^2

(x-9/2)^2=- 12 + 81/4

WriteAsFrac

Write as a fraction

(x-9/2)^2=- 48/4 + 81/4

AddFrac

Add fractions

(x-9/2)^2=33/4

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt((x-9/2)^2)=sqrt(33/4)

CalcRoot

Calculate root

x-9/2=± sqrt(33/4)

RootQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

x-9/2=± sqrt(33)/2

AddEqn

LHS+9/2=RHS+9/2

x=9/2± sqrt(33)/2

The solutions for this equation are x= 92± sqrt(33)2. Let's separate them into the positive and negative cases.

x=9/2± sqrt(33)/2
x_1=9/2 + sqrt(33)/2	x_2=9/2 - sqrt(33)/2
x_1=9 + sqrt(33)/2	x_2=9 - sqrt(33)/2
x_1≈ 7.4	x_2≈ 1.6

We found that the solutions of the given equation are x_1≈ 7.4 and x_2≈ 1.6.