heres a little warm up for you wonderful math masters?

Question

5-5
Solve each equation by using square roots property
2)x squared -12x + 36 =25
4)9x2squared-24x+16=2
Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.
8) x squared-12x+c
Solve each equation by completing the square

10) xsquared + 3x -18=0
12) 2x squared- 3x-3=0
14) x squared+2x+6=0
Solve each equation by competing the square
16) x squared +4x+4=25
18) x squared-9x+81/4=1/4
20)x squared +8x+16=7
22) x squared +12x +36 =5
Find the value of c that makes each trinomial a perfect square then write it as a perfect trinomial square
24) x squared + 16x+c
26) x squared -5x +c
Solve each equation by completing the square
28) x squared -8x+15=0.
30) x2 +2x-6=0
32) 2xsquared +3x-5=0
34) 2x squared +7x +6=0
36) x squared-4x +5=0
38) x squared-10x+28=0

Answer 1

If you teacher couldn't even do it, what makes you think I can?

Answer 2

if a trinomial (ax^2 + bx + c) is a perfect square, then the middle term (b) will be twice the square root of a times the square root of c. When a is 1, this is simply: is 1/2 of the b equal to square root of c.

2)x^2 -12x + 36 =25
Here 1/2 of -12 = -6; -6 squared = 36, so this is a perfect square.
solving the problem:
(x-6)^2 = 5^2
x-6 = +/-5
x = 1, 11

4)9x2 -24x + 16=2
Here the a term is not 1, sqrt of 9 = 3; sqrt of 16 = 4; twice 3*4 = 12, so this is a perfect square.
(3x - 4)^2 = 2
(3x-4) = sqrt(2)
3x = 4 +/- sqrt(2)
x = (4 + sqrt2)/3, (4 - sqrt2)/3


Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.
8) x^2 -12x +c
We had this in problem 2 above
half of 12 is 6; 6^2 = 36 = c
x^2 - 12x + 36

Solve each equation by completing the square

Here, we force the c term to be what it needs to be to make the trinomial a perfect square. We'll need to add or subtract from each side of the equation

10) x^2 + 3x -18=0
1/2 of 3 = 1.5 and 1.5 squared is 2.5
x^2 + 3x + 20.5 - 18 = 20.5
x^2 + 3x + 2.5 = 20.5
(x+1.5)^2 = 20.5
x + 1.5 = sqrt(20.5)
x = -1.5 + sqrt(20.5), -1.5 - sqrt(20.5)

12) 2x^2 - 3x -3=0
2 isn't part of a perfect square, so let's divide everything by 2 first
x^2 - 1.5x - 1.5 = 0
1/2 of 1.5 = .75; .75 squared = .5625 (9/16)
x^2 - 1.5x - 1.5 + 2.0625 = 2.0625
(x - .75)^2 = 2.0625
x = .75 +/- sqrt(2.0625)
x = 3/4 +/- sqrt(33/16)
x = 3/4 +/- sqrt33)/4
x = (3 + sqrt33)/4 , (3 - sqrt33)/4

14) x^2 +2x + 6=0
x^2 + 2x + 1 = -5
(x+1)^2 = -5
(x+1) = +/-i*sqrt5
x = -1 - i*sqrt5, -1 + i*sqrt5
where i is the square root of -1

Solve each equation by competing the square
16) x^2 +4x +4=25
(x +2)^2 = 25
x + 2 = sqrt25 = 5
x = -2 +/-5 = -7, 3

18) x^2 -9x +81/4 = 1/4
(x - 9/2)^2 = (1/2)^2
x - 9/2 = +/- 1/2
x = 9/2 +/- 1/2 = 5, 4

20)x^2 +8x +16 = 7
(x + 4)^2 = 7
x + 4 = +/- sqrt7
x = -4 + sqrt7, -4 - sqrt7

22) x^2 +12x +36 =5
(x+6)^2 = 5
x + 6 = +/- sqrt5
x = -6 - sqrt5, -6 + sqrt5

Find the value of c that makes each trinomial a perfect square then write it as a perfect trinomial square
24) x^2 + 16x+c
take half of the b term and square it. 1/2 of 16 = 8; 8^2 = 64
x^2 + 16x + 64

26) x^2 -5x +c
1/2 of 5 = 5/2; 5/2 squared = 25/4
x^2 - 5x + 25/4

Solve each equation by completing the square
28) x^2 -8x+15=0
x^2 -8x + 15 + 1 = 1
(x -4)^2 = 1
x-4 = +/-1
x = 4 +/-1 = 3, 5

30) x^2 +2x -6=0
x^2 + 2x -6 + 7 = 7
(x +1)^2 = 7
x +1 = +/- sqrt7
x = sqrt7 -1; -sqrt7 -1

32) 2x^2 +3x-5=0
either multiply everything by 2 or divide everything by 2 to make the first term a perfect square; let's multiply
4x^2 + 6x - 10 = 0
the c term needs to be +9/4 to get 6x in the b term
4x^2 + 6x -10 + 10 + 9/4 = 10 + 9/4 = 49/4
(2x +3/2)^2 = (7/2)^2
2x + 3/2 = +/- 7/2
2x = 7/2 - 3/2, -7/2 - 3/2 = 2, -5
x = 1, - 2.5

34) 2x^2 +7x +6=0
4x^2 + 14x + 12 = 0
14/2 = 7 need to divide by 2 again to take care of the sqrt4, so the c term needs to be (7/2)^2
4x^2 + 14x + 12 -12 + 49/4 = -12 + 49/4 = 1/4
4x^2 + 14x + 49/4 = 1/4
(2x + 7/2)^2 = (1/2)^2
2x + 7/2 = +/-1/2
2x = -1/2 - 7/2, -1/2 + 7/2
2x = -4, 3
x = -2, 3/2

36) x^2 -4x +5=0
x^2 - 4x +4 = -1
(x-2)^2 = -1
x-2 = +/- i
x = 2 + i, 2 - i

38) x^2 -10x +28 = 0
x^2 - 10x + 25 = -3
(x -5)^2 = -3
x-5 = +/-i*sqrt3
x = 5 + isqrt3, 5 - isqrt3

Answer 3

Solve each equation by using square roots property

2)x squared -12x + 36 =25
x^2 - 12x + 11

x-11 x-1
x=11 or x=1

4)9x2squared-24x+16=2
9x^2 - 24x + 14

Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.
8) x squared-12x +36

Solve each equation by completing the square
x^2 + 3x -18=0

x^2 + 3x + 2.25= 18 + 2.25
(x + 1.5)^2= 20.25
x + 1.5= square root of20.25 - 1.5
x= 4.5 - 1.5 and 4.5 + 1.5=
x= 3 or x=6

Answer 4

Methinks someone wants us to do homework.

As a hint, doing the first one using square roots will look like this:

x^2 - 12x + 36 = 25

(x-6)(x-6) = 25
(x-6)^2 = 25
(x-6)^2 = 5^2

Take the square root on both sides (not forgetting about the +/- thing):

+/-(x-6) = +/- 5

There are two cases to consider (the other two being equal by symmetry)

A: (x-6) = 5
B: (x-6) = -5

The other cases being
-(x-6) = -5 (same as A)
-(x-6) = 5 (same as B)

Answer 5

each and every little bit facilitates Suzie - we could continuously purchase a number of those pills for all of the farm animals in Oklahoma and Texas - then the country could be seen as CONTRIBUTING to cleansing up our surroundings! LOL CJ

Answer 6

Thats alot of questions !!!!!!!

Answer 7

HA......HA

Answer 8

very funny.................