Solve the following equations by using the method of completing t… - Vidyadip

Question

Solve the following equations by using the method of completing the square:
$5x^2 - 6x - 2 = 0$

✓

Answer

$5x^2 - 6x - 2 = 0 $
$\Rightarrow 25x^2 - 30x - 10 = 0$ (Multiplying both sides by 5)
$\Rightarrow 25x^2 - 30x = 10$
$\Rightarrow (5x)^2 - 2 \times 5x \times 3 + 3^2 = 10 + 3^2$ [Adding $3^2$ on both sides]
$\Rightarrow (5x - 3)^2 = 10 + 9 = 19$ $\Rightarrow\text{5x}-3=\pm19$ (Taking square root on both sides)$\Rightarrow\text{5x}-3=\sqrt{19}$ or $\text{5x}- 3=-\sqrt{19}$
$\Rightarrow\text{5x}=3+\sqrt{19}$ or $\text{5x}=3-\sqrt{19}$
$\Rightarrow\text{x}=\frac{3+\sqrt{19}}{5}$ or $\text{x}=\frac{3-\sqrt{19}}{5}$
Hence, $\frac{3+\sqrt{19}}{5}$ and $\frac{3-\sqrt{19}}{5}$ are the roots of the given equation.

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