Exercise 30 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. - 4x^2+8x+44=16 ⇔ - 4x^2+8x=- 28 Now let's divide each side by - 4 so the coefficient of x^2 will be 1. - 4x^2+8x=- 28 ⇓ x^2-2x=7 In 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=7

AddEqn

LHS+1=RHS+1

x^2-2x+ 1=7+ 1

FacPosPerfectSquare

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

(x-1)^2=7+1

AddTerms

Add terms

(x-1)^2=8

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt((x-1)^2)=sqrt(8)

CalcRoot

Calculate root

x-1=± sqrt(8)

▼

Simplify right-hand side

Write as a product

x-1=± sqrt(4* 2)

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

x-1=± sqrt(4)* sqrt(2)

CalcRoot

Calculate root

x-1=± 2sqrt(2)

AddEqn

LHS+1=RHS+1

x=1± 2sqrt(2)

Both x=1+2sqrt(2) and x=1-2sqrt(2) are solutions of the equation.