Fill in the blank with a number to make the expression a perfect square
$x^{2} - 6 x + ?$

Question

Fill in the blank with a number to make the expression a perfect square  x2−6x+?

Ayesha Gomez · Accepted Answer

Step 1
We find a number to make the expression a perfect square
$x^{2} - 6 x + ?$
Step 2
We Identify b then we find ${(\frac{b}{2})}^{2}$
$∵ {(\frac{- 6}{2})}^{2} = 9$
We add ${(\frac{b}{2})}^{2} = 9$ in $e q u a t i o n^{n}$ , we get perfect square
$x^{2} - 6 x + 9$
$\Rightarrow {(x - 3)}^{2}$
$∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}$
Hence
$x^{2} - 6 x + 9$

star233 · Accepted Answer

In a perfect square trinomial, the first term is the square of a binomial, the second term is twice the product of the two terms in the binomial, and the last term is the square of the second term.
Let's start by finding the binomial. Since the coefficient of

x^{2}

is 1, we know that the binomial will have the form

x + a

, where

a

is a constant.
The square of this binomial is

(x + a)^{2} = x^{2} + 2 a x + a^{2}

.
Comparing this with the given expression

x^{2} - 6 x + ?

, we can see that

a^{2}

represents the missing term.
To find

a

, we look at the coefficient of the linear term

x

in the given expression, which is -6. We can observe that

2 a x

is the same as

- 6 x

, so

2 a = - 6

.
Dividing both sides of the equation

2 a = - 6

by 2, we find that

a = - 3

.
Now we can determine the missing term by squaring

a

:

a^{2} = (- 3)^{2} = 9

Therefore, the missing term is 9.
Thus, the expression

x^{2} - 6 x + ?

can be made a perfect square by adding 9 to it.
The complete expression, with the missing term filled in, is

x^{2} - 6 x + 9

.

alenahelenash · Accepted Answer

To make the expression x2−6x+? a perfect square, we need to find the missing number that, when added to the expression, will result in a perfect square trinomial.A perfect square trinomial can be written in the form (x−a)2, where a is a constant. By expanding (x−a)2, we get x2−2ax+a2. Comparing this to the given expression x2−6x+?, we can determine that −2ax should be equal to −6x, which means a=3.Therefore, the missing number that should be added to the expression is a2, which is 32=9. Hence, the complete expression to make it a perfect square is x2−6x+9.

user_27qwe · Accepted Answer

Result: 9Solution:To determine the missing number, we can use the formula for expanding a perfect square, which is (x−a)2=x2−2ax+a2. Comparing this with the given expression, we can see that −2ax=−6x, which implies 2a = 6 or a = 3.Now, we substitute the value of &#039;&#039;a&#039;&#039; into the expanded form and find the missing number:(x−a)2=x2−2ax+a2=x2−2(3)x+32=x2−6x+9Therefore, the missing number that completes the expression x2−6x+? to make it a perfect square is 9.

Fill in the blank with a number to make the expression a perfect square x

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