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2x^2-10x-1=0, complete the square?

+2 votes
List the missing value after completing the square.
asked Jan 18, 2013 in ALGEBRA 1 by anonymous Apprentice

1 Answer

+2 votes

2x2 – 10x – 1 = 0

Separate variables and constants aside by adding 1 from each side 

2x2 – 10x = 1

Here x2 coefficient is 2, for perfect square make x2 coefficient 1. 
Divide each side by 2

x2 - 5x = ½


To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

Here x coefficient = -5. So, (half the x coefficient)² = (-5/2)2= 25/4

Add 25/4 to each side 
x2 - 5x + 25/4 = ½ + 25/4

(x – 5/2) 2= 27/4

Take square root both sides 

x – 5/2 = ±√27/4

x – 5/2 = ±(3√3)/2

Add 5/2 to each side

x = 5/2 ±(3√3)/2

x = (5 ± 3√3) / 2

answered Jan 18, 2013 by John Lyn Pupil

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