Solve 3x² - 4x+1=0using completing the square
Answer (1)
Answer:[tex]3 {x}^{2} - 4x + 1 = 0 \\ \\ 3 {x}^{2} - 4x + 1 = 0 \\ \frac{3 {x}^{2} }{3} - \frac{4x}{3} + \frac{1}{3} = 0 \\ {x}^{2} - \frac{4}{3} x + \frac{1}{3} = 0 \\ {x}^{2} - \frac{4}{3} x = - \frac{1}{3} \\ \\ = {( \frac{b}{2}) }^{2} \\ = {( \frac{ \frac{ - 4}{3} }{2}) }^{2} \\ = {( - \frac{4}{3} \div 2 )}^{2} \\ = {( - \frac{4}{3} \times \frac{1}{2} )}^{2} \\ = {(- \frac{4}{6} )}^{2} \\ = - \frac{ {4}^{2} }{ {6}^{2} } \\ = \frac{16}{36} \\ \\ {x}^{2} - \frac{4}{3} x + \frac{16}{36} = - \frac{1}{3} + \frac{16}{36} \\ {x}^{2} - \frac{4}{3}x + \frac{16}{36} = \frac{ - 12 + 16}{36} \\ {x}^{2} - \frac{4}{3}x + \frac{16}{36} = \frac{4}{36} \\ {(x - \frac{4}{6} )}^{2} = \frac{4}{36} \\ \sqrt{{(x - \frac{4}{6} )}^{2}} = \sqrt{ \frac{4}{36} } \\ x - \frac{4}{6} = ± \frac{2}{6} \\ x = \frac{4}{6} ± \frac{2}{6} \\ \\ x_{1} = \frac{4}{6} + \frac{2}{6} \: \: \: \: \: \: \: \: \: \: \: x_{2} = \frac{4}{6} - \frac{2}{6} \\ x_{1} = \frac{6}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x_{2} = \frac{2}{6} \\ x_{1} = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x_{2} = \frac{1}{3} [/tex]Step-by-step explanation:medyo mahaba sya, pero ganyan talaga kapag completing the square. sana makatulong. have a nice day!
