Page 713 - Algebra 1

Exploration Modeling Completing the Square
Algebra tiles are used to visualize the process of completing the square. Use
algebra tiles to model x2 + 4x.
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a. Can these tiles be used to form a square? Explain.
b. What type of tile could be added to form a square? How many are
needed? Make a drawing.
c. What is the value of the tiles in this square?
d. What is the factored form of the trinomial? What is the length of a side of the square?
e. Write Does the sign of the coefficient of the x-term determine the sign of the constant? Explain.
Completing the square is used to solve quadratic equations. Once the square is completed, the equation is solved by finding the square root of both sides.
Solving x2 + bx = c by Completing the Square Solve by completing the square.
Math Reasoning
Analyze How would the drawing be different for completing the square of x2 - 4x?
Example
2
a. x2+10x=11 SOLUTION
Complete the square.
x2 +10x=11 x2 + 10x + = 11
_2 _2 x2 +10x+(10)=11+(10) 22
x2 +10x+(5)2 =11+(5)2 x2 +10x+25=11+25
(x+5)2 =36 Solve using square roots.
2
x+5=±6 x+5=-6 or x+5=6
-__5 = -__5 -__5 = -__5 x = -11 or x = 1
Complete the square. Add the missing value to both sides of the equation.
Simplify the fraction.
Simplify.
Factor the left side. Simplify the right side.
Take the square root of both sides of the equation.
Simplify.
Write as two equations. Subtraction Property of Equality Simplify.
Math Reasoning
Analyze Why is 25 added to both sides of the equation?
Hint
The square root of a number squared is that number. So, √ (x + 5 )2 = √( x + 5)( x + 5)
= (x + 5).
698 Saxon Algebra 1
√ √(x+5) =± 36
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