Question

Please help worth 10 points​ picture attached

Answer 1

36

13

20

Explanation:

x²+12x+(_)

(x)²+2(x)(6)+6²

So, 6² which is 36

z²-10z+12+(_)

(z)²-2(z)(5)+5²

5² = 25 = 12 + _

So additional term is 13

k²+(_)k+100

k²+(_)k+10²

k²+2(k)(10)+10²

k²+20k+100

So, missing number is 20

Answer 2

1. 36

2. 13

3. 20

Explanation:

1. x^2 + 12x + _

Let y the value that will be added to make it a perfect square.

x^2 + 12x + y

Using the formula:

b^2 = 4ac

a = 1, b = 12, c = y

12^2 = 4 x 1 x y

144 = 4y

Divide both side by 4

y = 144/4 = 36

2. z^2 — 10z + 12 + _

Let b be what will make the expression perfect.

z^2 — 10z + (12 + b)

z^2 — 10z + c

a = 1, b = —10, c =?

b^2 = 4ac

(—10)^2 = 4 x 1 x c

100 = 4b

Divide both side by 4

c = 100/4 = 25

c = 12 + b

b = c — 12

b = 25 — 12

b = 13

3. k^2 + _K + 100

b^2 = 4ac

a = 1, b =? , c = 100

b^2 = 4 x 1 x 100

b^2 = 400

Take the square root of both side

b = √400

b = 20