Question

How do you complete the square of: 4x^2 - 24x + 11 = 0

Answer 1

The same way you normally do it; do you know how to complete the square? :)

Answer 2

no I'm kind of confused by it.. thats why I'm asking:)

Answer 3

fair enough.

The first step you might perform to complete the square is to divide both sides by the coefficient of the \( x^2 \) term

after doing that, the equation looks like \(x^2 - 6x + \frac{11}{4} = 0\)

Answer 4

next step is to move the constant term to the right side, so in our case we subtract both sides by \( \frac{11}{4} \) to get \[x^2 - 6x = -\frac{11}{4}\]

Answer 5

to complete the square from this step, we should add both sides by a constant term so that the left side can be reduced to a perfect square. That constant term is always equal to \( \frac{b^2}{4} \) (ignoring the sign). In our equation, our b is equal to 6 so we can add \( \frac{36}{4} = 9\) to both sides to get \[x^2 - 6x + 9 = -\frac{11}{4} + 9\]

Answer 6

the left hand side is now a perfect square, so we can reduce is to \((x - 3)^2 \)

Answer 7

the reply to the ans i by simply factorization (2x-1)(2x-11)

Answer 8

that works, but I thought the question asked us to use the procedure of completing the square to find out those roots.

Answer 9

oh didnt knw about that

Answer 10

are u good in maths?

Answer 11

after completing the square using the steps above and simplifying the right hand side, our equation becomes \[(x-3)^2 = \frac{25}{4}\] to solve the equation just take the square root of both sides and solve for x in both cases.

Answer 12

me? nope :( when I was in school I didn't know how to complete the square either :-P