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Solve the equation 2x2 - 5x + 3 by the method of completing the square method.

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2 Answers

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2x^2-5x+3=0

x^2-5/2x+3/2=0

x^2-2/2×5/2=-3/2

x^2-2×5/4=-3/2

x^2-2×5/4+(5/4)^2=-3/2+(5/4)^2

(x-5/4)^2=-3/2+25/16

(x-5/4)^2=1/16

x-5/4=+1/4,-1/4

x=5/4+1/4,5/4-1/4

x=3/2,1
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2x2 - 5x + 3 = 0

2x2/2 - 5x/2 + 3/2 = 0 (dividing both sides by 2)  

x2 - 5x/2 + 3/2 = 0

[x2 - 5x/2 + (5/4)2] - (5/4)2 + 3/2 = 0

[x - 5/4]2 - 25/16 + 3/2 = 0

[x - 5/4]2 - (25-24)/16 = 0

[x - 5/4]2 - 1/16 = 0

[x - 5/4]2 = 1/16

x - 5/4 = ± 1/4   (square rooting on both sides)  

x = 1/4 + 5/4  or x = -1/4 + 5/4

x = (1+5)/4   or x = (-1+5)/4

x = 6/4   or x = 4/4

x = 3/2  or  x = 1

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