Question

5x²=4x+7 solve by using completing squre method

Answer 1

5x^2 = 4x + 7

=> 5x^2 - 4x = 7

=> x^2 - 4x/5 = 7/5

=> x^2 - 4x/5 + (2 /5)^2 = 7/5 + (2/5)^2

=> ( x - 2/5)^2 = 7/5 + 4/25

=> (x - 2/5)^2 = ( 39/25)

=> x - 2/5 = sqrt ( 39 /25)

$x - \frac{2}{5} = + - \frac{ \sqrt{39} }{5} \\ \\ x = \frac{2}{5} + - \frac{ \sqrt{39} }{5} \\ \\ \alpha = \frac{2 + \sqrt{39} }{5} \\ \\ \beta = \frac{2 - \sqrt{39} }{5}$