Question

Find the roots of 4xsq+3x+5=0 by the method of completing the square

Answer 1

$4x^{2} + 3x + 5 = 0$

$(2x)^{2} + 2(2x)( \frac{3}{4} ) + ( \frac{3}{4} ) ^{2} - (\frac{3}{4} )^{2} + 5 = 0$

$(2x + \frac{3}{4} )^{2} = ( \frac{3}{4} )^{2} - 5$

$(3x + \frac{3}{4} )^{2} = \frac{9}{16} - 5$

$(3x + \frac{3}{4} )^{2} = \frac{9 - 90}{16}$

$(3x + \frac{3}{4} )^{2} = ( \frac{ - 81}{16} )$

$(3x + \frac{3}{4} ) = \sqrt{} \frac{ - 81}{16}$

$(3x + \frac{3}{4} ) = \frac{ - 9}{4}$