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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

6. Segment Relationships in Circles

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Exercise 27 Page 574

To complete the square make sure all the variable terms are on one side of the equation. Then, calculate the value of ( b2 )^2.

x_1=5, x_2=- 9

Practice makes perfect

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+4x=45 In a quadratic expression b is the linear coefficient. For the equation above, we have that b=4. Let's now calculate ( b2 )^2.

( b/2 )^2

b= 4

( 4/2 )^2

Calculate quotient

2^2

Calculate power

4

Next, we will add ( b2 )^2=4 to both sides of our equation. Then, we will factor the trinomial on the left-hand side and solve the equation.

x^2+4x=45

LHS+4=RHS+4

x^2+4x+ 4=45+ 4

FacPosPerfectSquare

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

(x+2)^2=45+4

Add terms

(x+2)^2=49

sqrt(LHS)=sqrt(RHS)

sqrt((x+2)^2)=sqrt(49)

Calculate root

x+2=± 7

LHS-2=RHS-2

x=- 2± 7

We got that there are two solutions to the equation. x_1&=- 2+7=5 x_2&=- 2-7=- 9

Subchapter links

Communicate Your Answer p.569

Monitoring Progress p.570-572