Math  /  Algebra

QuestionComplete the Square. Fill in the number that makes the polynomial a perfect-square quadratic. x2+18x+x^{2}+18 x+ \square Divided by ÷\div

Studdy Solution

STEP 1

1. We are given a quadratic expression x2+18x+ x^2 + 18x + \square .
2. We need to find the constant term that makes this expression a perfect square trinomial.
3. A perfect square trinomial is of the form (x+a)2=x2+2ax+a2 (x + a)^2 = x^2 + 2ax + a^2 .

STEP 2

1. Identify the coefficient of the linear term.
2. Calculate the value needed to complete the square.
3. Fill in the blank with the calculated value.

STEP 3

Identify the coefficient of the linear term in the expression x2+18x+ x^2 + 18x + \square .
The coefficient of the linear term x x is 18 18 .

STEP 4

To complete the square, take half of the coefficient of the linear term and square it.
Calculate half of 18 18 :
182=9 \frac{18}{2} = 9
Now, square the result:
92=81 9^2 = 81

STEP 5

Fill in the blank with the calculated value to make the expression a perfect square trinomial.
The expression becomes:
x2+18x+81 x^2 + 18x + 81
This is equivalent to:
(x+9)2 (x + 9)^2
The number that completes the square is 81 \boxed{81} .

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord