solve 2xsquare -5x+3=0 by the method of compleing square
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2x² - 5x + 3 = 0
2(x² - 5x/2 + 3/2) = 0
x² - 5x/2 + 3/2 = 0
x² - 2/2(x)(5/2) = -3/2
x² - 2(x)(5/4) = -3/2
adding (5/4)² on both sides,
x² - 2(x)(5/4) + (5/4)² = -3/2 + (5/4)²
(x - 5/4)² = -3/2 + 25/16
(x - 5/4)² = -24+25/16
(x - 5/4)² = 1/16
(x - 5/4) = ±√1/16
(x - 5/4) = ±1/4
x = 5/4 ± 1/4
x = (5±1)/4
x = 5+1/4 = 6/4 = 3/2
x = 5-1/4 = 4/4 = 1
the roots are 3/2 and 1
2(x² - 5x/2 + 3/2) = 0
x² - 5x/2 + 3/2 = 0
x² - 2/2(x)(5/2) = -3/2
x² - 2(x)(5/4) = -3/2
adding (5/4)² on both sides,
x² - 2(x)(5/4) + (5/4)² = -3/2 + (5/4)²
(x - 5/4)² = -3/2 + 25/16
(x - 5/4)² = -24+25/16
(x - 5/4)² = 1/16
(x - 5/4) = ±√1/16
(x - 5/4) = ±1/4
x = 5/4 ± 1/4
x = (5±1)/4
x = 5+1/4 = 6/4 = 3/2
x = 5-1/4 = 4/4 = 1
the roots are 3/2 and 1
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The value of x is "-1". For Expiation of the same please view the above picture
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