Question

X^2 + 1/2x + = 2 +
Help please

Answer 1

Step 2:

For Completing the square,

`((1)/(2) coefficient\ x)^(2) =((1)/(2)* (1)/(2))^(2)=(1)/(16)`

Add half coefficient of x square on both the side we get

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

Explanation:

Solve:

`2x^(2)+x-4=0`

`2x^(2)+x=4`

Solution:

Step 1:

Dividing both the side by two we get

`x^(2)+(x)/(2)=2`

Step 2:

For Completing the square,

`((1)/(2) coefficient\ x)^(2) =((1)/(2)* (1)/(2))^(2)=(1)/(16)`

Add half coefficient of x square on both the side we get

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

Step 3:

We know
`(a +b)^(2) = a^(2)+2ab +b^(2)`

`(x+(1)/(4))^(2)=(33)/(16) \\ \\(x+(1)/(4))=\pm \sqrt{(33)/(16)} \\\\x=-(1)/(4)\pm \sqrt{(33)/(16)}`