Question

I really need help! This is last minute and its 1 am. I'm tired so I'm going to leave it to you guys to solve my problems and provide statistical explanations. Please help me and answer these before 9: 15 in the morning EST on March 3rd, 2020.

Answer 1

Answer:

Step-by-step explanation:

1) n² - 20n - 96 = 0

n² - 20n + (- 20/2)² = 96 + (- 20/2)²

(n - 10)² = 96 + 100

(n - 10)² = 196

Taking square root of both sides

n - 10 = √196 = 14

n = 14 + 10

n = 24

2) x² + 12x = 48

x² + 12x + (12/2)² = 48 + (12/2)²

(x + 6)² = 48 + 36 = 84

Taking square root of both sides,

x + 6 = 9.2

x = 9.2 - 6

x = 3.2

3) x² - 14x + 40 = 0

x² - 14x = - 40

x² - 14x + (- 14/2)² = - 40 + (- 14/2)²

(x - 7)² = - 40 + 49 = 9

Taking square root of both sides,

x - 7 = 3

x = 3 + 7

x = 10

4) 5b² - 20b - 18 = 7

5b² - 20b = 7 + 18

5b² - 20b = 25

Dividing both sides by 5, it becomes

b² - 4b = 5

b² - 4b + (-4/2)² = 5 + (-4/2)²

(b - 2)² = 5 + 4 = 9

Taking square root of both sides

b - 2 = 3

b = 3 + 2

b = 5

Answer 2

Answer:

question 1

$n^{2} - 20n -96 = 0$

use product and sum method

product = -96

sum = -20

numbers needed = ( -24 , 4)

n - 24 = 0

n + 4 = 0

hence n = 24 and n = -4

Question 2

$x^{2} + 12 x = 48$

in the form $ax^{2} +bx +c = 0$

= $x^{2} +12x - 48$

make use of the formula :

$\frac{-b+-\sqrt{b^{2} -4ac} }{2a}$

replace values to make 2 equations :

1.$\frac{-12+\sqrt{12^{2} -4*1*-48} }{2*1}$ = 3.17

2.$\frac{-12-\sqrt{12^{2} -4*1*-48} }{2*1}$ = -15.2

hence x = 3.17 and x = -15.2

Question 3

$x^{2} -14x+40=0$

use product and sum method

product = 40

sum = -14

numbers needed = (-10 , -4)

x - 10 = 0

x - 4 = 0

hence x = 10 and x = 4

Question 4

$5b^{2} -20b-18 = 7$

in the form $ax^{2} +bx +c = 0$

this becomes $5b^{2} -20b-18-7$

= $5b^{2} -20b-25$

can simplify by 5

= $b^{2} -4b-5 =0$

use product and sum method

product = -5

sum = -4

numbers needed (-5 , 1)

b-5 = 0

b + 1 = 0

hence b = 5 and b = -1