Determine a number that must be added to make each of the following a perfect square trinomial.
1. x² + 12x + ___
2. x² - 14x + ___
3. x² + 22x + ___
4. x² - 5x + ___
5. x² + ⅔x + ___
1. x² + 12x + ___
2. x² - 14x + ___
3. x² + 22x + ___
4. x² - 5x + ___
5. x² + ⅔x + ___
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Answer:
1. 36
2. 49
3. 121
4. 25/4
5. 1/9
Step-by-step explanation:
1. x² + 12x + __
to get the constant term, identify the values of a, b and c
a = 1 b = 12 c = ?
to get the value of c, divide the value of b to 2, then multiply it by itself
12/2 = 6
6 x 6 = 36
c = 36
2. x² - 14x + __
a = 1 b = -14 c = ?
-14/2 = -7
-7 x -7 = 49
c = 49
3. x² + 22x + __
a = 1 b = 22
22/2 = 11
11 x 11 = 121
c = 121
4. x² - 5x + __
a = 1 b = -5
-5/2 = -5/2
(-5/2) x (-5/2) = 25/4
c = 25/4
5. x² + ⅔x + __
a = 1 b = ⅔
(⅔) ÷ 2 = ⅔ x ½ = 2/6 = ⅓
⅓ x ⅓ = ⅑
c = ⅑
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