Find the roots of the equation $5 x^{2} - 6 x - 2 = 0$ by the method of completing the square.

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x = 5

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x = 3

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Solution

The correct option is B
Multiplying the equation throughout by 5, we get $25 x^{2} - 30 x - 10 = 0$
This is the same as:
$(5 x)^{2} - 2 \times (5 x) \times 3 + 3^{2} - 3^{2} - 10 = 0$
$\Rightarrow (5 x - 3)^{2} - 9 - 10 = 0$
$\Rightarrow (5 x - 3)^{2} - 19 = 0$
$\Rightarrow (5 x - 3)^{2} = 19$
$\Rightarrow 5 x - 3 = \pm \sqrt{19}$
$\Rightarrow x = \frac{3 \pm \sqrt{19}}{5}$

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