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.
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
Originally posted by Lee012lee: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 ?
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.
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 ?
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)
Originally posted by ƒlame: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
Originally posted by Lee012lee: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 ?
Originally posted by ƒlame: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
PS : We can use the formula a^2 + 2ab + b^2 = (a +b)^2 tooOriginally posted by Lee012lee: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
Originally posted by ƒlame: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.
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
Originally posted by qdtimes2: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.
Originally posted by Lee012lee: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 -
question already states that Express x2 + 11x - 15 in the form (x+a)2 + b so its -15
how do u get -35.25 .
isnt it -15 -30.25 =45.25?
Originally posted by qdtimes2: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.
Originally posted by bratorbread: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.