Question

5x^2 - 6x - 2 = 0 By completing the square Method. (Solution)​

Answer 1

Given,

$\boxed{\sf{5x^2-6x-2=0}}$

The squares can be equated from the equation:

$\boxed{\bold{\sf{x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}}}}$

Here,

• a = 5
• b = -6
• c = -2

$\implies \sf{x=\dfrac{6 \pm \sqrt{6^2-(4\times 5\times 2)}}{2\times 5}}$

$\implies \sf{x=\dfrac{6 \pm \sqrt{36+40}}{10}}$

$\implies \sf{x=\dfrac{6 \pm \sqrt{76}}{10}}$

$\implies \sf{x=\dfrac{6 \pm 2\sqrt{19}}{10}}$

Dividing by 2:

$\implies \sf{x=\dfrac{3 \pm \sqrt{19}}{5}}$

$\implies \sf{x=\dfrac{3 + \sqrt{19}}{5} \ \ \ \ \ \&\ \ \ \ \ \sf{x=\dfrac{3 - \sqrt{19}}{5}}}$

$\boxed{\bold{\implies \sf{x=\dfrac{3 + \sqrt{19}}{5} \ \ \ \ \& \ \ \ \ \ \sf{x=\dfrac{3 - \sqrt{19}}{5}}}}}$