Solving by Completion of Squares Method

Q.

Solve the equation $3x^2-5x+2=0$ by completing the square method.

Q.

A motor boat has a speed of 18 $\frac{km}{hr}$ in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in $km/hr.$

1. $5km/hr$

2. $7km/hr$

3. $4km/hr$

4. $6km/hr$

Q.

Solve the equation 5$x^2$– 6$x$– 2 = 0 by the method of completing the square. Find the positive root.

1. $x$= $\frac{3+\sqrt{19}}{5}$

2. $x$= $\frac{3+\sqrt{17}}{5}$

3. $x$= $\frac{3-\sqrt{19}}{5}$

4. $x$= $\frac{3+\sqrt{17}}{5}$

Q.

A student says that if $5x^2=20$, then $x$ must be equal to $2$. do you agree or disagree with the student? justify your answer.

Q.

Which of the following operations could make the expression $x^2+\frac{8x}{\sqrt{3}}$ a perfect square?

1. $Add(\frac{8}{\sqrt{3}}{)}^2$

2. $Add(\frac{4}{\sqrt{3}}{)}^2$

3. $Add(\frac{8}{3}x{)}^2$

4. $Subtract\frac{8x}{\sqrt{3}}$

Q.

Solve the quadratic equation 4$x^2$+ 5$x$ = 0 by completion of squares method. In the given options one of the options has one root and also the converted form of equation after completing the square. Select this option

1. x= 0, - =0

2. = , - =0

3. = , -=0

4. = , - =0

Q.

Find the square of the following : $0.1x+0.3y$

Q.

What number should be added to ${9x}^2$ + 18 $x$ to make it a perfect square?

Q.

What are the roots of the quadratic equation $(x+2{)}^2$-16 = 0?

1. $x$ = 2 or -6

2. $x$ = -2 or 6

3. $x$ = 2 or 6

4. $x$ = -2 or -6

Q. There are three figures of areas $x^2,12x$ and $z$ in the below figure. Figures A and C are squares while figure B is a rectangle, with length of one side as $x.$ What should be the value of $z$ so that all the 3 figures can be arranged to form a square of side (x +6)?

1. 16
2. 36
3. 24
4. 18

Q.

What number should be added to $x^2+6x$ to make it a perfect square?

1. 9

2. 72

3. 36

4. 18

Q.

The product of 2 consecutive natural numbers is 56. Solve this problem using completing the square method of quadratic equation. Write the equation obtained after completing the square and also write the smaller of the 2 numbers.

1. 7, $(x+\frac{1}{2}{)}^2-\frac{225}{4}=0$

2. 7, $(x-\frac{1}{2}{)}^2-\frac{225}{4}$ = 0

3. 8, $(x+\frac{1}{2}{)}^2–\frac{225}{4}=0$

4. 8, $(x-\frac{1}{2}{)}^2-\frac{225}{4}=0$

Q.

Using the method of completion of squares find one of the roots of the equation $2x^2-7x+3=0$. Also, find the equation obtained after completion of the square.

1. 6

2. 12

3. 13

4. 3