Home > Algebra > Completing the Square

How do you complete the square for #3x^2 +18x + 5#?

Answer 1

Eli Assouline

#3(x+3)^2-22#

#3x^2+18x+5#

take out common factor to make coefficient #x^2=1#

#=3(x^2+6x)+5#

now CTS within the bracket as usual, as shown below

#=3(x^2+6x+3^2-3^2)+5#

#=3((x+3)^2-9)+5#

#=3(x+3)^2-27+5#

#=3(x+3)^2-22#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Abigail Allen

#3(x + 3)^2 - 22#

Before completing the square a must equal 1, so first we divide all terms by 3.

= #(3x^2)/3 + (18x)/3 + (5)/3#

= #3(x^2 + 6x + 5/3)#

= #3(x^2 + 6x +(6/2)^2 - (6/2)^2 + 5/3)#

= #3((x^2 + 6x + 9) - 9 + 5/3)#

= #3((x^2 + 6x + 9) - 27/3 + 5/3)#

= #3((x^2 + 6x + 9) - 22/3)#

#(x^2 + 2xy + y^2) = (x + y)^2#, so...

= #3((x + 3)^2 - 22/3)#

= #3(x + 3)^2 - 22#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Eli Assouline

To complete the square for the quadratic expression (3x^2 + 18x + 5), follow these steps:

Factor out the coefficient of (x^2) (which is 3): (3(x^2 + 6x) + 5).
Take half of the coefficient of (x) (which is 6), square it, and add it inside the parentheses: (3(x^2 + 6x + 9) - 27 + 5).
Simplify inside the parentheses: (3(x + 3)^2 - 27 + 5).
Combine like terms: (3(x + 3)^2 - 22).

So, the expression, completed by square, is (3(x + 3)^2 - 22).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.