SOLUTION: State the value(s) of k that make each of the following a perfect square. A)25x^2-70x+k B)x^2+x+k C)81x^2+kx+36 D)kx^2-48x+64 Thank you in advance.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: State the value(s) of k that make each of the following a perfect square. A)25x^2-70x+k B)x^2+x+k C)81x^2+kx+36 D)kx^2-48x+64 Thank you in advance.      Log On


   

Question 826089: State the value(s) of k that make each of the following a perfect square.
A)25x^2-70x+k
B)x^2+x+k
C)81x^2+kx+36
D)kx^2-48x+64
Thank you in advance.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A.
25x%5E2-70x%2Bk=0
%2825x%5E2-70x%29%2Bk=0 complete the square

%2825x%5E2-70x%2B+_+%29+-+_+%2Bk=0 add a number in parentheses and then subtract it after parentheses
%2825x-70x%2B49%29-49%2Bk=0
%285x-7%29%5E2-49%2Bk=0 => k=49
so, the perfect square is %285x-7%29%5E2=0%7D%7D%5D+which+is+equal+to+%0D%0A%0D%0A%7B%7B%7B25x%5E2-70+x%2B49 in expanded form

B.
x%5E2%2Bx%2Bk=0
%28x%5E2%2Bx%29%2Bk=0 complete the square
%28x%5E2%2Bx%2B1%2F4%29-1%2F4%2Bk=0
%28x%2B1%2F2%29%5E2-1%2F4%2Bk=0 => k=1%2F4
so, the perfect square is %28x%2B1%2F2%29%5E2=0%7D%7D%5D+which+is+equal+to+%0D%0A%0D%0A%7B%7B%7Bx%5E2%2Bx%2B1%2F4=0 in expanded form
C)
81x%5E2%2Bkx%2B36 or
%289x%29%5E2%2Bkx%2B6%5E2...as you can see, k is equal to a product of 2%2A9 and 6 which is k=108
so,
%289x%29%5E2%2B108x%2B36=%289x%2B6%29%5E2

I hope you can do the last one following these examples....