Question

To complete the square of $x^2-3x$ , add$\_\_\_\_\_\_$ .

Short answer

To complete the square of$x^2-3x$, addrole="math" localid="1646794628543" $\frac{\mathbf{9}}{\mathbf{4}}$.

Step-by-step solution

Step 1. Given information.

Given Expression:

$x^2-3x$

We want to complete the square of the given expression with the missing terms.

Step 2. Solution

What it actually means to complete a square is to find a number $a$that when added to the given expression enables the whole expression, including the added number, to be written as a square like in the following example:

$x^2-3x+a={(x+b)}^2$

First expand the right side of the equality $x^2+bx+b^2$.

Both sides of the equality are polynomials and even more, they are equal.

Therefore, coefficients in front of the same power of the variable $x$must be the same.

Forrole="math" localid="1646795833717" $x^2:1=1$the quality obviously holds. Moving on to$x:-3=2b$

Therefore $b=-\frac{3}{2}$. And finally $a=b^2={(-\frac{3}{2})}^2=\frac{9}{4}$

Step 3. Conclusion:

Therefore, in order to complete the square add $\frac{9}{4}$to the expression. You can check if the answer is correct by finding the square:$x^2-3x+\frac{9}{4}={(x-\frac{3}{2})}^2$