Question

solve the quadratic equation 3x^2+5x+1=0 by method of completing the square​

Answer 1

$Given:-$

• $Quadratic \: equation :- \sf{3x^2 - 5x + 2}$

$To \: find:-$

• $Value \: of \: x \: by \: completing \: the \: square \: method.$

$Solution:-$

$\sf{⇢3x^2 - 5x + 2}$

$Divide \: the \: equation \: by \: 3$

$⇢ {3x}^{2}/{3} - {5x}/{3} + {2}/{3} = 0$

$⇢ {x}^{2} - {5x}/{3} + {2}/{3} = 0$

$Add \: ({5}/{6})^{2} \: on \: both \: side \: of \: the \: equation.$

$⇢ {x}^{2} - 5x/3 + 25/36 = -2/3 + 25/36$

$⇢ ({x }+ {5}/{6})^{2} = {-2}/{3} + {25}/{36}$

$⇢ ({x} + {5}/{6})^{2} = {-24 + 25}/{36}$

$⇢ ({x} + {5}/{6})^{2} = {1}/{36}$

$⇢ \sf {x} + {5}/{6} = \sqrt[- +]\frac{1}{36}$

$⇢ \sf {x} = {1}/{6} - {5}/{6}$

$⇢ \sf {x} = {-4}/{6}$

$⇢ \sf {x} = {-2}/{3}$

$Or$

$⇢ \sf {x} = {-1}/{6} - {5}/{6}$

$⇢ \sf {x} = {-6}/{6}$

$⇢ \sf {x} = {-1}$

$x = 1 \: \: \: or \: \: \: x = \sf {-2}{3}$

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