Question

X2 + 1 2 x +__ = 2 + __ ?
PLEASE HELPP

Answer 1

`\[ x^2 + (1)/(2)x + (1)/(4) = 2 + (1)/(4) \]`

Let's fill in the blanks for the equation
`\(x^2 + (1)/(2)x + ? = 2 + ?\)`:

To balance the equation, we need to add terms to both sides. Let's complete the square on the left side:

`\[ x^2 + (1)/(2)x + \left((1)/(4)\right) = 2 + \left((1)/(4)\right) \]`

Now, the expression on the left side is a perfect square trinomial:

`\[ \left(x + (1)/(2)\right)^2 = (9)/(4) \]`

So, filling in the blanks:

`\[ x^2 + (1)/(2)x + (1)/(4) = 2 + (1)/(4) \]`

The equation is now balanced.