Question

solve the following quadratic equation by the method of perfect the square 5x^2-6x-2=0​

Answer 1

Answer:

see the answer above

Step-by-step explanation:

hope it helps you

Answer 2

Answer :

The roots are :

{3 + (√19)}/5 and {3 - (√19)}/5

Given :

The quadratic equation :

• 5x² - 6x - 2 = 0

Task :

• To solve the equation by the method of perfect square (or completing square)

Solution :

Given ,

5x² - 6x - 2 = 0

Dividing both the side by 5 we have

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

Now adding 9/25 on both the sides we have :

$\sf \implies x^{2} - 2\times x \times (\dfrac{3}{5}) + \dfrac{9}{25} - \dfrac{2}{5} = \dfrac{9}{25} \\\\ \sf \implies x^{2} - 2(x) \dfrac{3}{5} + (\dfrac{3}{5})^{2} = \dfrac{9}{25} + \dfrac{2}{5} \\\\ \sf \implies (x - \dfrac{3}{5})^{2} = \dfrac{9 + 10}{25} \\\\ \sf \implies \sf x - \dfrac{3}{5} = \pm \sqrt{\dfrac{19}{25}} \\\\ \sf \implies x = \dfrac{3}{5} \pm \dfrac{\sqrt{19}}{5} \\\\ \sf \implies x = \dfrac{3 \pm \sqrt{19}}{5}$

Thus the roots of the equation are :

$\bf \dfrac{3+\sqrt{19}}{5} \: \: and \: \: \dfrac{3 - \sqrt{19}}{5}$