Po is trying to solve the following equation by completing the square: $$49x^2+56x-64 = 0.$$he successfully rewrites the above equation in the following form: $$(ax + b)^2 = c,$$where $a$, $b$, and $c$ are integers and $a > 0$. what is the value of $a + b + c$?

The question is...

Po is trying to solve the following equation by completing the square: 49x^2+56x-64 = 0. He successfully rewrites the above equation in the following form: (ax + b)^2 = c,where a, b and c are integers and a > 0. What is the value of a + b + c?

3.122

Step-by-step explanation:

49x^2+56x-64 = 0

49(x^2+56x/49) - 64 = 0

49(x^2+8x/7) = 60

introduce a new constant to form (ax+b)^2 form from the multiplier of x

New constant = ((8/7) ÷ 2)^2

= (8/14)^2

Put the constant into equation plus another equal constant with negative value

49(x^2 + 8x/7 + (8/14)^2 - (8/14)^2) = 60

Reduce the following part

x^2 + 8x/7 + (8/14)^2 = (x + 8/14)^2

Put back into equation:

49((x + 8/14)^2) - 49(8/14)^2 = 60

49((x + 8/14)^2) = 60 + 49(8/14)^2

= 60 + 49(64/196)

= 60 + 16 = 76

(x + 8/14)^2 = 76/49

Equating with (ax + b)^2 = c

a = 1, b = 8/14, c = 76/49

a + b + c = 1 + 8/14 + 76/49 = 3.122

y + 11 = (1/4)(x + 16)

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.