Question

What number must be added to the expression below to complete thesquare?x²-x

Answer 1

SOLUTION:

Step 1:

In this question, we are given the following:

What number must be added to the expression below to complete the

square?

x²-x

Step 2:

Steps in completing the square method are as follows:

$\begin{gathered} \text{Given } \\ \text{x }^2\text{ - x} \\ We\text{ can s}ee\text{ that:} \\ \text{coefficient of x}^2\text{ = 1} \\ \text{Divide through by 1, we have that:} \\ x^2\text{ - x} \\ \text{Next:} \\ \text{coefficient of x = -1} \\ \text{Divide by 2, we have: }\frac{-1}{2} \\ Square\colon\text{(}\frac{-1}{2})^2\text{ =}\frac{1}{4} \end{gathered}$

Step 3:

From step 2, we can see that:

$\begin{gathered} \frac{1}{4}\text{ will be added to:} \\ x^2\text{ - x, } \\ \text{we have that:} \\ x^2-x\text{ + (}\frac{1}{4})^{}\text{ = ( x -}\frac{1}{2})^2 \end{gathered}$

CONCLUSION:

$\begin{gathered} \frac{1}{4}\text{ is the number that must be added to the expression: } \\ x^2-\text{ x to complete the square} \end{gathered}$