Question

Solve quadratic equation by completing square method x2+x-20=0

Answer 1

$x^{2} + x - 20 = 0$

${x}^{2} + x = 20$

${x}^{2} + 2\times x \times \frac{1}{2} = 20$

${x}^{2} + 2 + x \times \frac{1}{2} = 20 + ( \frac{1}{2})^{2}$

$(x + \frac{1}{2} )^{2} = 20 + \frac{1}{4}$

$(x + \frac{1}{2}) ^{2} =\frac{80 + 1}{4}$

$(x +\frac{1}{2})^{2} = \frac{81}{4}$

$(x +\frac{1}{2} ) = \pm\frac{\sqrt81}{4}$

$(x+\frac{1}{2} ) = \pm\frac{9}{2}$

$x + \frac{1}{2}+\frac{9}{2} \: or \: x + \frac{1}{2} - \frac{9}{2}$

$x =\frac{8}{2}\: or\: x = \frac{-10}{2}$

$\implies\ x = 4 \:or \:x = - 5$