Solve the equation by completing the square 16x^2+1=! i can't completely factor x^2-7/16x-7/! can anyone me i need so bad on this ! : (

Hello from MrBillDoesMath!

Discussion:

The original equation is  16x^2 + 1 = 7x. Subtracting 7x from each side, and then dividing by 16, gives

x^2 - (7/16)x  + 1/16  = 0

Recall that  (x -a)^2 = x^2 -2ax + a^2 is the form of a perfect square.   So dividing (7/16) by 2 gives 7/32 which is the quantity we need to square and add to make a perfect square:

x^2 - (7/16)x + (7/32)^2 -  (7/32)^2 + 1/16 = 0

or

(x - 7/32)^2               =  (7/32)^2 + 1/16

Final hint:  (7/32)^2 + 1/16  =  113\1024

Hope this helps.

Regards, MrB

a. 3/4 ÷ 1/8 = 6

step-by-step explanation:

in the question, the number line represents 3/4 divided into 6 equal units. each arrow represents a unit and there are a total of six arrows.

the size of each unit is 1/8 as shown.

showing that 1/8 divides 3/4 into 6 divisions:

3/4 ÷ 1/8

= 3/4 x 8/1

= 3/1 x 8/4

= 3 x 2

= 6

hence, the number line represents six divisions given by 3/4 ÷ 1/8.

22

step-by-step explanation: