Question

5x²-бx-2 =0 complete the square​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer :

x = ( 3 ± √19 ) / 5

Given :

• 5x² - бx - 2 =0

To Find :

• Solve equation using completing square method.

Solution :

$\sf 5x^2-6x-2=0$

Dividing the equation by 5 on both sides , we get ,

$\implies \sf x^2-\dfrac{6}{5}x-\dfrac{2}{5}=0\\\\\implies \sf x^2-2.x.\dfrac{3}{5}-\dfrac{2}{5}=0$

Compare middle term 2.x.3/5 with 2ab in a² - 2ab + b² , we get ,

b = 3/5 .So add and subtract (3/5)² .

$\implies \sf x^2-2.x.\dfrac{3}{5}+\bigg(\dfrac{3}{5}\bigg)^2-\bigg(\dfrac{3}{5}\bigg)^2-\dfrac{2}{5}=0\\\\\implies \sf \bigg(x-\dfrac{3}{5}\bigg)^2=\dfrac{9}{25}+\dfrac{2}{5}\\\\\implies \sf \bigg(x-\dfrac{3}{5}\bigg)^2=\dfrac{(9+10)}{25}\\\\\implies \sf \bigg(x-\dfrac{3}{5}\bigg)^2=\dfrac{19}{25}\\\\\implies \sf x-\dfrac{3}{5}=\pm\dfrac{\sqrt{19}}{5}\\\\\implies \bf x=\dfrac{3\;\pm \;\sqrt{19}}{5}$