Question
Solve the following equations by using the method of completing the square:
$x^2 + 8x - 2 = 0$
$x^2 + 8x - 2 = 0$
✓
Answer
$x^2 + 8x - 2 = 0$
$\Rightarrow x^2 + 8x = 2$
$\Rightarrow x^2 + 2 \times x \times 4 + 4^2 = 2 + 4^2 (Adding 4^2 on both sides)$
$\Rightarrow (x + 4)^2= 2 + 16 = 18$
$\Rightarrow\text{x}+4=\pm\sqrt{18}=\pm3\sqrt2$ (Taking square root on both sides)
$\Rightarrow\text{x}+4=3\sqrt2$ or $\text{x}+4=-3\sqrt2$
$\Rightarrow\text{x}=-4+3\sqrt2$ or $\text{x}=-4-3\sqrt2$
Hence, $\big(-4+3\sqrt2\big)$ and $\big(-4-3\sqrt2\big)$ are the roots of the given equation.
$\Rightarrow x^2 + 8x = 2$
$\Rightarrow x^2 + 2 \times x \times 4 + 4^2 = 2 + 4^2 (Adding 4^2 on both sides)$
$\Rightarrow (x + 4)^2= 2 + 16 = 18$
$\Rightarrow\text{x}+4=\pm\sqrt{18}=\pm3\sqrt2$ (Taking square root on both sides)
$\Rightarrow\text{x}+4=3\sqrt2$ or $\text{x}+4=-3\sqrt2$
$\Rightarrow\text{x}=-4+3\sqrt2$ or $\text{x}=-4-3\sqrt2$
Hence, $\big(-4+3\sqrt2\big)$ and $\big(-4-3\sqrt2\big)$ are the roots of the given equation.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Solve the following systems of equations:
$\frac{5}{\text{x}+\text{y}}-\frac{2}{\text{x}-\text{y}}=-1,$
$\frac{15}{\text{x}+\text{y}}+\frac{7}{\text{x}-\text{y}}=10.$
→$\frac{5}{\text{x}+\text{y}}-\frac{2}{\text{x}-\text{y}}=-1,$
$\frac{15}{\text{x}+\text{y}}+\frac{7}{\text{x}-\text{y}}=10.$
If the point A(2, -4) is equidistant from P(3, 8) and Q(-10, y), find the values of y. Also find distance PQ.
Construct a triangle with sides 5 cm 6 cm and 7 cm and then another triangle whose sides are $\frac{3}{5}$ of the corresponding sides of the first triangle.
→Solve the following quadratic equations by factorization:
$\frac{\text{a}}{\text{x}-\text{a}}+\frac{\text{b}}{\text{x}-\text{b}}=\frac{2\text{c}}{\text{x}-\text{c}}$
→$\frac{\text{a}}{\text{x}-\text{a}}+\frac{\text{b}}{\text{x}-\text{b}}=\frac{2\text{c}}{\text{x}-\text{c}}$
Red queens and black jacks are removed from a pack of playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is
(i) a king
(ii) of red colour
(iii) a face card
(iv) a queen
(i) a king
(ii) of red colour
(iii) a face card
(iv) a queen
A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Solve for x and y:$\frac{5}{\text{x}+\text{y}}-\frac{2}{\text{x}-\text{y}}=-1,$
$\frac{15}{\text{x}+\text{y}}+\frac{7}{\text{x}-\text{y}}=10$
→$\frac{15}{\text{x}+\text{y}}+\frac{7}{\text{x}-\text{y}}=10$
In the given figure, APB and AQO ar semicircles and AO = OB. if the perimeter of the figure is 40cm, find the area of the shaded region.
Weights of new born babies in a hospital are as follows:
If the mode of the data is 2.2 kg, find the unknown frequency x.
| Weight (in kg) | 1.3-1.5 | 1.5-1.7 | 1.7-1.9 | 1.9-2.1 | 2.1-2.3 | 2.3-2.5 | 2.5-2.7 | 2.7-2.9 |
| Number of new born babies | 1 | 4 | 6 | 9 | 10 | x | 8 | 3 |
If the mode of the data is 2.2 kg, find the unknown frequency x.