Question

I need to show how to find these solutions 1/4 and 3/4 by completing the square!

Help please!

Answer 1

See explanation, and ask for more details if unclear!

Explanation:

The perfect square of this equation is
`x^2-x+(1)/(4)`, since the square would be
`(x-(1)/(2))^2`. 1/4=4/16, meaning that you can set up the equation in the following way:

`(x^2-x+(1)/(4))-(1)/(16)=0`

`(x-(1)/(2))^2=(1)/(16)`

Take the square root of both sides:

`x-(1)/(2)=\pm (1)/(4)`

Add 1/2 to both sides:

`x=(1)/(2)\pm (1)/(4)=(3)/(4), (1)/(4)`. Hope this helps!

Answer 2

see below

Explanation:

x^2 - x + 3/16 = 0

Subtract 3/16 from each side

x^2 - x + 3/16 - 3/16 = -3/16

x^2 -x = -3/16

Take the coefficient of x

-1

Divide by 2

-1/2 call this a

Square it

(-1/2)^2 = 1/4

Add it to each side

x^2 - x +1/4 =- 3/16+1/4

Changing to the "square"

( x +a)^2 = - 3/16+1/4

getting a common denominator

( x -1/2) ^2 = -3/16+ 4/16

( x -1/2) ^2 =1/16

Take the square root of each side

sqrt( ( x -1/2) ^2) = ± sqrt(1/16)

x -1/2 = ± 1/4

Add 1/2 to each side

x -1/2 + 1/2 = 1/2 ± 1/4

x = 1/2 ± 1/4

Separate into 2 equations

x = 1/2 + 1/4 x = 1/2 - 1/4

2/4 +1/4 2/4 -1/4

3/4 1/4