Exercise 28 Page 574

We want to solve the quadratic equation by completing the square. To do so, we will start by rewriting the equation so all terms with x are on one side of the equation. x^2-2x-1=8 ⇔ x^2-2x=9In a quadratic expression b is the linear coefficient. For the equation above, we have that b=- 2. Let's now calculate ( b2 )^2.

( b/2 )^2

Substitute

b= - 2

( - 2/2 )^2

CalcQuot

Calculate quotient

(- 1)^2

CalcPow

Calculate power

1

Next, we will add ( b2 )^2=1 to both sides of our equation. Then we will factor the trinomial on the left-hand side and solve the equation.

x^2-2x=9

AddEqn

LHS+1=RHS+1

x^2-2x+ 1=9+ 1

FacPosPerfectSquare

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

(x-1)^2=9+1

AddTerms

Add terms

(x-1)^2=10

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt((x-1)^2)=sqrt(10)

CalcRoot

Calculate root

x-1=± sqrt(10)

AddEqn

LHS+2=RHS+2

x=1± sqrt(10)

Both x=1+sqrt(10) and x=1-sqrt(10) are solutions of the equation.