Question
Solve the following equations by using the method of completing the square:
$5x^2 - 6x - 2 = 0$
$5x^2 - 6x - 2 = 0$
✓
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.
$\Rightarrow 25x^2 - 30x - 10 = 0$ (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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3x + 2y + 25 = 0,
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From this $d =$ $\square$ and $a =$ $\square$
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$t_{20}=\square$
Amount of simple interest after 20 years is $=$ $\square$
→$\text { Simple interest }=\frac{P \times R \times N}{100}$
Simple interest after 1 year $=\frac{1000 \times 10 \times 1}{100}=\square$
Simple interest after 2 year $=\frac{1000 \times 10 \times 2}{100}=\square$
Simple interest after 3 year $=\frac{\square \times \square \times \square}{100}=300$
According to this the simple interest for $4,5,6$ years will be 400, $\square$ $\square$ respectively.
From this $d =$ $\square$ and $a =$ $\square$
Amount of simple interest after 20 years
$t_n+a+(n-1) d $
$t_{20}=\square+(20-1) \square $
$t_{20}=\square$
Amount of simple interest after 20 years is $=$ $\square$
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