Question

5. Solving equations by completing the square!
r^2+2r-33=0. 6. a^2-2a-48=0

Answer 1

@wolf1728

Answer 2

please help me!

Answer 3

Solve Quadratic Equation by Completing The Square

2.2 Solving r2+2r-33 = 0 by Completing The Square .

Add 33 to both side of the equation :
r2+2r = 33

Now the clever bit: Take the coefficient of r , which is 2 , divide by two, giving 1 , and finally square it giving 1

Add 1 to both sides of the equation :
On the right hand side we have :
33 + 1 or, (33/1)+(1/1)
The common denominator of the two fractions is 1 Adding (33/1)+(1/1) gives 34/1
So adding to both sides we finally get :
r2+2r+1 = 34

Adding 1 has completed the left hand side into a perfect square :
r2+2r+1 =
(r+1) • (r+1) =
(r+1)2
Things which are equal to the same thing are also equal to one another. Since
r2+2r+1 = 34 and
r2+2r+1 = (r+1)2
then, according to the law of transitivity,
(r+1)2 = 34

We'll refer to this Equation as Eq. #2.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of
(r+1)2 is
(r+1)2/2 =
(r+1)1 =
r+1

Now, applying the Square Root Principle to Eq. #2.2.1 we get:
r+1 = √ 34

Subtract 1 from both sides to obtain:
r = -1 + √ 34

Since a square root has two values, one positive and the other negative
r2 + 2r - 33 = 0
has two solutions:
r = -1 + √ 34
or
r = -1 - √ 34

Answer 4

r^2+2r-33=0

To complete the square:
Move the "non X" term to the right:
r^2+2r=33

Divide the equation by the coefficient of X² which in this case is 1 so there's no change
r^2+2r=33

Now for "completing the square" we:
take the coefficient of X which is 2
divide that by 2
1
square that number
1
then add it to both sides of the equation
r^2+2r +1=34

Take the square root of BOTH sides of the equation
(r+1) = sqrt(34)

r = sqrt(34) -1

site explaining completing the square:
http://www.1728.org/quadr2.htm

Answer 5

Solving a2-2a-48 = 0 by Completing The Square .

Add 48 to both side of the equation :
a2-2a = 48

Now the clever bit: Take the coefficient of a , which is 2 , divide by two, giving 1 , and finally square it giving 1

Add 1 to both sides of the equation :
On the right hand side we have :
48 + 1 or, (48/1)+(1/1)
The common denominator of the two fractions is 1 Adding (48/1)+(1/1) gives 49/1
So adding to both sides we finally get :
a2-2a+1 = 49

Adding 1 has completed the left hand side into a perfect square :
a2-2a+1 =
(a-1) • (a-1) =
(a-1)2
Things which are equal to the same thing are also equal to one another. Since
a2-2a+1 = 49 and
a2-2a+1 = (a-1)2
then, according to the law of transitivity,
(a-1)2 = 49

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of
(a-1)2 is
(a-1)2/2 =
(a-1)1 =
a-1

Now, applying the Square Root Principle to Eq. #3.2.1 we get:
a-1 = √ 49

Add 1 to both sides to obtain:
a = 1 + √ 49

Since a square root has two values, one positive and the other negative
a2 - 2a - 48 = 0
has two solutions:
a = 1 + √ 49
or
a = 1 - √ 49

Answer 6

i really don't get it!

Answer 7

i am so confused all i see are numbers!

Answer 8

@ganeshie8

Answer 9

Gee I got bounced out of here a while ago and I see cutepochacco finished the OTHER question!!!
Wow - that is fast !!
So you want some explanation baby456?

Answer 10

yes please

Answer 11

Gee I can't really explain why completing the square works

Answer 12

its ok ! i guess i will watch some youtube videos!

Answer 13

okay - they might tell you the how but not WHY it works.

Answer 14

its okay i will learn! bye!

Answer 15

okay good luck :-)