Transcript Warm Up 5.2.3 More Completing the Square

5-83. Solve each quadratic equation below by completing the square. You may
use algebra tiles or draw a diagram to represent the tiles. Write your answers in exact
form. Then explain how you can determine how many solutions a quadratic equation has
once it is written in perfect square form.
a. x2 – 6x + 7 = 0
x2 – 6x
= -7
x2 – 6x + 9 = 2
(x – 3)2 = 2
|x – 3| = 2
x – 3 = 2 or x – 3 = - 2
b. p2 + 2p + 1 = 0
(p + 1)2 = 0
|p + 1| = 0
p+1=0
p = -1
c. k2 – 4k + 9 = 0
k2 – 4k
= -9
k2 – 4x + 4 = -5
(k – 2)2 = -5
|k – 2| = −5
No Real Solution
x = 3 + 2 or 3 – 2
5-84. Instead of using algebra tiles, how can you use an area model to complete the
square for each equation in problem 5-83? Show your work clearly.
5.2.3 MORE COMPLETING
THE SQUARE
January 27, 2016
Objectives
• CO: SWBAT solve quadratic equations
by first rewriting the quadratic in
perfect square form.
• LO: SWBAT generalize the process of
completing the square.
5-85. Jessica wants to complete the square to rewrite x2 + 5x + 2 = 0 in perfect square
form. First, she rewrites the equation as x2 + 5x = –2. But how can she split the five x-tiles
into two equal parts?
Jessica decides to use force! She cuts one x-tile in half and starts to build a square from
the tiles representing x2 + 5x, as shown below.
a. How many unit tiles are missing
from Jessica’s square?
6.25
b. Help Jessica finish her problem by
writing the perfect square form of
her equation.
(x + 2.5)2 = 4.25
5-86. Examine your work in problems 5-84 and 5-85 and compare the
standard form of each equation to the corresponding equation in perfect
square form. For example, compare x2 – 6x + 7 = 0 to (x – 3)2 = 2.
a. What patterns can you identify that are true for every pair of
equations?
The number in the parenthesis is always half of the x-term. The number
added to each side is square the number that is halved.
b. When a quadratic equation in standard form is changed to
perfect square form, how can you predict what will be in the
parentheses? For example, if you want to rewrite x2 + 10x –
3 = 0 in perfect square form, what will the dimensions of the
square be?
x+5
Add 25 to each side
5-87. Use the patterns you found in problem 5-86 to help you rewrite
each equation below in perfect square form and then solve it.
a. w2 + 28w + 52 = 0
w2 + 28w
= - 52
(w + 14)2 = 144
|w + 14| = 12
w + 14 = 12 or w + 14 = -12
w = -2 or w = -26
c. k2 − 16k = 17
(k – 8)2 = 81
|k – 8| = 9
k – 8 = 9 or k – 8 = -9
k = 17 or k = -1
b. x2 + 5x + 4 = 0
x2 + 5x
=-4
(x + 2.5)2 = 2.25
|x + 2.5| = 2.25
x + 2.5 = 1.5 or x + 2.5 = -1.5
x = -1 or x = -4
d. x2 − 24x + 129 = 0
x2 – 24x
= -129
(x – 12)2 = 15
|x – 12| = 15
x – 12 = 15 or x – 12 = - 15
x = 12 + 15 or 12 – 15
x ≈ 15.87 or 8.13