Question

Find the roots of the quadratic equation $2x^2+5x+3=0$ by the method of completing the square.

Answer 1

Given that,
$2x^2+5x+3=0$

Multiplying the equation by $8$, we get

$16x^2+2\times 5\times 4x+24=0$

$(4x{)}^2+2\times 5\times 4x+25-25+24=0$

$(4x+5{)}^2-1^2=0$

$(4x+5-1)(4x+5+1)=0$

$(4x+4)(4x+6)=0$

$x=-1,\frac{3}{2}$

Hence, this is the answer.