Complete the square for the following, but do not solve:
x^2 - 4x = 0
(x -2)^2 = 4
100
John factored something as the following. What are the solutions to the problem?
(x + 2) (x -3) = 0
x = -2 or x = 3
100
When do you get an answer of no real solutions when using the quadratic formula?
Square root of 0.
200
Factor the following:
z^2 - 81
(z + 9)(z-9)
200
When do you get an answer with a square root in it?
Square root is not a whole number
200
When would you get "no real solutions" as an answer to a problem when completing the square?
When you are taking the square root of a negative?
200
Suzanne factored a problem, but needs help finding the solutions:
x(2x - 1) = 0
x = 0 or x = 1/2
200
If you cannot factor a problem, is your answer no real solutions? Why or why not?
No, could just have a fractional or square root answer.
300
Factor the following:
3m^2 - 27
3(m-3)(m+3)
300
Identify a, b, and c for the following:
3x^2 - 2x + 9 = 18
a = 3, b = -2, c = -9
300
Complete the square for the following, but do not solve:
3x^2 - 6x - 9 = 0
(x - 1)^2 = 4
300
Frank completed the square and go the following. Help him find the answers:
(x + 3)^2 = 9
x = 0 or x = -6
300
When would you get only one answer when using the quadratic formula?
Square root of 0.
400
Factor the following:
81s^2 + 18s + 1
(9s + 1) (9s + 1)
400
What is your answer when b^2 -4ac is negative?
No real solutions
400
Is it possible to get only one solution to a problem when completing the square? Why or why not?
Yes, if you are taking the square root of 0.
400
George completed the square to get the following. What should be his answers?
(x + 2/3)^2 = 9/4
x = 5/6 or x = -13/6
400
When would your answer to a completing the square problem have a square root in the answer?
When the square root is not a whole number.
500
Factor the following:
4x^2 + 4x - 3
(2x+3 )(2x-1)
500
Use the quadratic formula to find the answer to the following:
10n^2 - 35 = 65n
n = -7 or n = 1/2
500
Complete the square for following, but do not solve:
3k^2 + 2k = 2
(k + 1/3)^2 = 5/9
500
After simplifying a little, Joanne got the following when using the quadratic formula. Finish simplifying it for her.
-7 +/- sqrt(121)
x = __________
7
x = 4/7 or x = -18/7
500
If you cannot factor a problem, how can you determine if it has no real solutions?
Use completing the square or quadratic formula methods
or graph it and see if it crosses the x-axis.