Question

What must be added to 9x
2
- 30x +22 to make it a whole square?

Answer 1

3 must be added to make perfect whole square

Answer 2

Answer:

We must add 3 to make it a whole square.

Step-by-step explanation:

We have been given the expression

$9x^2-30x+22$

We can rewrite this as

$(3x)^2-2\cdot3x\cdot5+22$

Now, we have the formula

$(a-b)^2=a^2-2ab+b^2$

The above expression is in the form if we have

$2ab = 2\cdot3x\cdot5$

It means we have

a = 3x

b = 5

Hence, b^2 = 5^2 =25

We have already 22, so we have to add 3 to make it 25

Thus, if we add 3 it will become

$(3x)^2-2\cdot3x\cdot5+22+3\\\\=(3x)^2-2\cdot3x\cdot5+25\\\\=(3x-5)^2$

This is a perfect square.

Hence, we must add 3 to make it a whole square.