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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Maintaining Mathematical Proficiency

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Exercise 9 Page 527

To complete the square, make sure all the variable terms are on one side of the equation.

w = - 1; w = 9

Practice makes perfect

We want to solve the quadratic equation by completing the square. Note that all terms with w are on one side of the equation.

w^2-8w=9
In a quadratic expression, b is the linear coefficient. For the equation above, we have that b=- 8. Let's now calculate ( b2 )^2.

( b/2 )^2

b= - 8

( - 8/2 )^2

▼

Simplify

Calculate quotient

( - 4 )^2

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.

w^2-8w=9

LHS+16=RHS+16

w^2-8w + 16 = 9 + 16

FacNegPerfectSquare

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

(w-4)^2 = 9 + 16

Add terms

(w-4)^2 = 25

sqrt(LHS)=sqrt(RHS)

sqrt((w-4)^2)=sqrt(25)

Calculate root

w-4 = ± 5

LHS+4=RHS+4

w = 4 ± 5

Both w= -1 and w=9 are solutions of the equation.

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Exercises p.527