Write the discriminant of the quadratic equation (x+5)^2=2(5x-3)
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Answer:
x 1 = 3
, x 2 = − 1 2
Explanation:
Completing the square means that you want to write
2 x 2 − 5 x − 3 = 0
on the form
( x − a ) 2 = b
First, let's get rid of the constant in front of the 2nd degree term:
x 2 − 5 2 x -3 2 = 0
We want this on the form
( x − a ) 2 = b
i.e. x 2 − 2 a x + a 2 = b
Comparing term for term, we see that
2 a = 5 2
, i.e.
a = 5 4
( x − 5 4 ) 2 = x 2 − 5 2 x + 25 16
We, therefore, have
( x 2 -5 2 x + 25 16 ) − 25 16 − 3 2 = 0
or
( x 2 − 5 2 x + 25 16 ) = 25 16 + 24 16 = 4916
( x − 5 4 ) 2 = ( 7 4 ) 2
x − 5 4 = ± 7 4 x = 5 4 ± 7 4
Therefore
x 1 -54 + 7 4 = 3
x 2 = 54 − 7 4
= − 1 2
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