Exercise 1 Page 579

We want to solve the quadratic equation by completing the square. Note that all the terms with x are on one side of the equation. x^2+8x=180 In a quadratic expression, b is the linear coefficient. For the equation above, we know that b=8. To change the expression x^2 + bx into a perfect-square trinomial, we need to add ( b2)^2 to this expression. Let's now calculate ( b2 )^2.

( b/2 )^2

Substitute

b= 8

( 8/2 )^2

CalcQuot

Calculate quotient

4^2

CalcPow

Calculate power

16

Next, we will add ( b2 )^2=16 to both sides of our equation. Then, we will factor the trinomial on the left-hand side, and solve the equation.

x^2+8x=180

AddEqn

LHS+16=RHS+16

x^2+8x+ 16=180+ 16

FacPosPerfectSquare

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

(x+4)^2=180+16

AddTerms

Add terms

(x+4)^2=196

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt((x+4)^2)=sqrt(196)

CalcRoot

Calculate root

x+4=± 14

SubEqn

LHS-4=RHS-4

x=- 4± 14

Let's write the exact solutions. x = - 4 ± 14 ⇔ x=- 18 x=10 Both x=- 18 and x=10 are solutions of the equation.