Question

desperate need of help
Using the factoring process, what constant is added to the RIGHT side of the quadratic equation 2x2 + 8x + ___ = 15 + ___ in order to solve by completing the square?

Answer 1

its 4 isnt it

Answer 2

2x2− 5x + ___ = 12 + ___

Answer 3

In order to complete a square, you need to have a coefficient of 1 for the x^2 term.
We can factor out a 2.

\(2x^2 + 8x + \_\_\_ = 15 + \_\_\_ \)

\(2(x^2 + 4x + \_\_\_) = 15 + \_\_\_\)

Now to complete the square, take half of the middle term coefficient and square it.
The middle-term coefficient is 4.
Take half of that and square it.
What do you get?

Answer 4

4

Answer 5

i need help with this one too 2x2− 5x + ___ = 12 + ___ i can't do fractions

Answer 6

i can post in as a new question so you can have two medals

Answer 7

Good.
Now we place a 4 in the first blank.

\(\color{green}{2}(x^2 + 4x + \color{red}{4}) = 15 + \_\_\_\)

Notice the factor of 2 outside the parentheses.
This means that the 4 after multiplying by 2 is really 8 that you are adding to the left side, so you need to add 8 to the right side.

\(\color{green}{2}(x^2 + 4x + \color{red}{4}) = 15 + \color{red}{8}\)

Answer 8

With your second problem, again, you need to factor out a 2 from the left side, so you have plain x^2, not 2x^2.

\(2x^2− 5x + \_\_\_ = 12 + \_\_\_ \)

\(2(x^2− \dfrac{5}{2}x + \_\_\_) = 12 + \_\_\_ \)

Now take the middle coefficient, \(\dfrac{5}{2} \).
Divide it by 2. Dividing by 2 is the same as multiplying by \(\dfrac{1}{2} \).
\(\dfrac{5}{2} \times \dfrac{1}{2} = \dfrac{5}{4} \)

Now square it: \(\dfrac{25}{16} \)

Now you add 25/16 to the left side inside the parentheses.

\(2(x^2− \dfrac{5}{2}x + \dfrac{25}{16}) = 12 + \_\_\_ \)

Once again, we have a factor of 2 outside the parentheses, so

\(2 \times \dfrac{25}{16} = \dfrac{25}{8} \)

That means we are really adding 25/8 to the left side, so we need to add 25/8 to teh right side.

\(2(x^2− \dfrac{5}{2}x + \dfrac{25}{16}) = 12 + \dfrac{25}{8} \)

Now we distribute the 2 on the left side:

\(2x^2− 5x + \dfrac{25}{8} = 12 + \dfrac{25}{8} \)