Question

. Solve the following equation by completing square. 11x2-34x+3=0

Answer 1

$x = 3 \: or \: \frac{1}{11}$

CALCULATION

$11 {x}^{2} - 34x + 3 = 0$

$11( {x}^{2} - \frac{34}{11} x + \frac{3}{11} ) = 0$

${x}^{2} - 2.x. \frac{17}{11} + {( \frac{17}{11} )}^{2} - {( \frac{17}{11} )}^{2} + \frac{3}{11} = 0$

${(x - \frac{17}{11} )}^{2} = \frac{289 - 33}{ {11}^{2} }$

${(x - \frac{17}{11} )}^{2} = \frac{ {16}^{2} }{ {11}^{2} }$

$(x-\frac{17}{11})=±\frac{16}{11}$

$x=\frac{17}{11}±\frac{16}{11}$

$x = \frac{17 + 16}{11} \: or \: \frac{17 - 16}{11}$

$x = \frac{33}{11} \: or \: \frac{1}{11}$

$x = 3 \: or \: \frac{1}{11}$