HELP

ƒlame SG

I need help with this question : Express x2 + 11x - 15 in the form (x+a)2 + b

and this 2 = square.

Thanks alot !

Eh another question ,

A wire of length 200cm is cut into two parts and each part is bent to form a square. If the area of the larger square is 9 times that of the smaller square, find the perimeter of the larger square.

Lee012lee SG

Method 1 (Completing the squares method)

Question

Express x^2 + 11x - 15 in the form (x+a)^2 + b

Solution

x^2 + 11x - 15

= x^2 + 11x + (11/2)^2 - (11/2)^2 - 15

= (x + 11/2)^2 - 45.25

Method 2 (Comparison Method)

Question

Express x^2 + 11x - 15 in the form (x+a)^2 + b

Solution

x^2 + 11x - 15 = (x+a)^2 + b

= x^2 + 2ax + a^2 + b

By comparison,

a = 11/2 and a^2 + b = - 15

Substitue a = 11/2 into

a^2 + b = - 15

(11/2)^2 + b = -15

b = - 45.25

x^2 + 11x - 15 = (x+a)^2 + b

= (x + 11/2)^2 - 45.25

ƒlame SG

Method 1 (Completing the squares method)

Question

Express x^2 + 11x - 15 in the form (x+a)^2 + b

Solution

x^2 + 11x - 15

= x^2 + 11x + (11/2)^2 - (11/2)^2 - 15

= (x + 11/2)^2 - 35.25

why do we need to plus (11/2)^2 and minus it ? shouldn't it be 0 then ?

Lee012lee SG

It is a step that helps us to make x^2 + 11x into a square by adding (11/2)^2 ie the reason why the method is called the completing the squares method.

We do not plus (11/2)^2 and minus it.

We will group x^2 + 11x + (11/2)^2 to make it into a square ie (x + 11/2)^2 while we just calculate the value of - (11/2)^2 - 15 to get a value of - 45.25.

ƒlame SG

so in the equation x^2 + 11x -15, to make it a perfect square, there must be a bx in the equation to solve it ?

Lee012lee SG

Question

A wire of length 200cm is cut into two parts and each part is bent to form a square. If the area of the larger square is 9 times that of the smaller square, find the perimeter of the larger square.

Steps

(1) Let the length of the small square be x cm

Let the length of the big square be y cm.

(2) The total of the two perimeters of the two sqaures will be equal to the length

of the wire ie

4x + 4y = 200

Divide by 4 throughout

x + y = 50

x = 50 - y --------------- Equation 1

(3) Given that the area of the larger square is 9 times that of the smaller square,

y^2 = 9x^2

Substitute x = 50 - y into

y^2 = 9x^2

y^2 = 9(50 - y)^2

y^2 = 9 (2500 -100y + y^2)

0 = 22500 - 900y + 9y^2 - y^2

0 = 22500 - 900y + 8y^2

y = 37.5 or 75

(4) When y = 37.5

Perimeter of the larger square = 4(37.5) = 150 cm

When y = 75 cm

Perimeter of the larger square = 4(75) = 300 cm (rejected as it cannot be

longer than the wire of 200 cm)

Lee012lee SG

so in the equation x^2 + 11x -15, to make it a perfect square, there must be a bx in the equation to solve it ?

Yes, there need to be a bx. However, even if there is no bx, we can always use 0x if necessary.

Please take note that there is a difference between

Express x^2 + 11x -15 into (x + a)^2 + b and

Solve x^2 + 11x -15 = 0

ƒlame SG

It is a step that helps us to make x^2 + 11x into a square by adding (11/2)^2 ie the reason why the method is called the completing the squares method.

We do not plus (11/2)^2 and minus it.

We will group x^2 + 11x + (11/2)^2 to make it into a square ie (x + 11/2)^2 while we just calculate the value of - (11/2)^2 - 15 to get a value of - 35.25.

I don't understand, what happens to the 11x ?

Lee012lee SG

I don't understand, what happens to the 11x ?

Use the trial and error method to factorise x^2 + 11x + (11/2)^2 into (x + 11/2)^2 .

However, most teachers will teach the students the cheating method ie

x^2 + 11x + (11/2)^2

(x + 11/2)^2

ƒlame SG

It is a step that helps us to make x^2 + 11x into a square by adding (11/2)^2 ie the reason why the method is called the completing the squares method.

We do not plus (11/2)^2 and minus it.

We will group x^2 + 11x + (11/2)^2 to make it into a square ie (x + 11/2)^2 while we just calculate the value of - (11/2)^2 - 15 to get a value of - 35.25.

Okay.... what do we need to put another 11/2^2 to calculate the value of (11/2)^2 - 15

Lee012lee SG

Okay.... what do we need to put another 11/2^2 to calculate the value of (11/2)^2 - 15

We cannot just add (11/2)^2 into an expression. So, we need to minus (11/2)^2 from the expression too.

qdtimes2 SG

for question 2, this method can acceptable or not?

Ratio of areas = Bigger : Smaller

9 : 1

Ratio of length of sides = Bigger : Smaller

3 : 1

The total length of the rope will be 4 units right,

so perimeter of the larger square = 200/4 x 3 = 150 cm

ƒlame SG

for question 2, this method can acceptable or not?

Ratio of areas = Bigger : Smaller

9 : 1

Ratio of length of sides = Bigger : Smaller

3 : 1

The total length of the rope will be 4 units right,

so perimeter of the larger square = 200/4 x 3 = 150 cm

Yeah why not.

yiha093 SG

We cannot just add (11/2)^2 into an expression. So, we need to minus (11/2)^2 from the expression too.

so no matter wat sign the qn say , the model is

-(11/2)^2 - 15 ?

then how know the 15 is + or -

ƒlame SG

question already states that Express x2 + 11x - 15 in the form (x+a)2 + b so its -15

bratorbread SG

how do u get -35.25 .

isnt it -15 -30.25 =45.25?

Lee012lee SG

for question 2, this method can acceptable or not?

Ratio of areas = Bigger : Smaller

9 : 1

Ratio of length of sides = Bigger : Smaller

3 : 1

The total length of the rope will be 4 units right,

so perimeter of the larger square = 200/4 x 3 = 150 cm

A good short-cut method to the question.

Thanks.

Lee012lee SG

how do u get -35.25 .

isnt it -15 -30.25 =45.25?

Sorry, I made a calculation mistake. Yes, the correct answer is 45.25.