SOLUTION: Given the quadratic equation x^2-15=2k(x-4),find k if there are two real and equal roots. I got k=5 and k=3 but I would appreciate it if someone could explain it in detail to me :)

SOLUTION: Given the quadratic equation x^2-15=2k(x-4),find k if there are two real and equal roots. I got k=5 and k=3 but I would appreciate it if someone could explain it in detail to me :)

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Question 118819: Given the quadratic equation x^2-15=2k(x-4),find k if there are two real and equal roots. I got k=5 and k=3 but I would appreciate it if someone could explain it in detail to me :) Thanks.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
expanding the equation gives x^2-15=2kx-8k ___ x^2-2kx+8k-15=0

for the quadratic to be a "perfect square", (b/2)^2=c ___ so (-2k/2)^2=8k-15

k^2-8k+15=0 ___ (k-5)(k-3)=0
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