please help me with this?

Question

1. Solve by factoring:
x^2 – 6x = -8



2. Solve using the square root property:
2x^2 – 3 = 15



3. Solve using the square root property:
(x + 7)^2 = 81



4. Solve by completing the square:
x^2 + 8x + 2 = 0

Answer 1

1.
x^2 - 6x + 8 = 0
(x-4)(x-2)=0.
S={2,4}.

2.
2x^2 - 3 = 15
2x^2 = 18
x^2 = 9
x= + or - √9
S={3,-3}.

3.
(x + 7)^2 = 81
√(x+7)^2 = +-√81
x + 7 = 9 OR x + 7 = -9
S={2, -16}.

4.
x^2 + 8x +2 = 0
x^2 + 8x = -2 now you must take 1/2 of b(8) and square it and you get 16... and add it to both sides...
x^2 + 8x + 16 = 14
(x+4)(x+4)=14
(x+4)^2=14
√(x+4)^2=√14
(x+4) = √14 OR (x+4) = -√14
S={√(14) - 4, -√(14) - 4}.

Answer 2

1.
Original equation:
x^2 - 6x = -8

Get it equal to zero
x^2 - 6x + 8 = 0

Factor it. -4 * -2 = 8, and - 4 + -2 = -6
(x - 4)(x - 2) = 0

Thus
x = 4, x = 2

2.
Original problem. By square root property, i guess you mean just solve for x and square root both sides?
2x^2 - 3 = 15

Add 3 to both sides
2x^2 = 18

Divide both sides by 2
x^2 = 9

Square root both sides
x = +/- 3
x = 3, x = -3

3.
Original Problem:
(x + 7)^2 = 81

Square root both sides
x + 7 = +/- 9

Subtract 7 from both sides
x = -7 +/- 9

And you get the two solutions.
x = -16, x = 2

4.
Original problem:
x^2 + 8x + 2 = 0

Subtract 2 from both sides
x^2 + 8x = -2

Now you need a number that when multiplied by 2, equals 8, that number is 4, so add 4^2 to both sides. (the reason 4^2 is because you will need it to the squared at the end in order for it to factor perfectly, fitting the formula (a + b)^2 = a^2 + 2ab + b^2 )
x^2 + 8x + 4^2 = 14

Now factor the perfect square
(x+4)^2 = 14

Square root both sides
x+4 = +/- sqrt(14)

Subtract 4
x = -4 +/- sqrt(14)
x = - 4 + sqrt(14), x = - 4 - sqrt(14)

Answer 3

1. Solve by factoring:
x^2 – 6x = -8
x^2 – 6x +8=0
(x - 4)(x - 2) = 0
x = {4, 2}
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
2. Solve using the square root property:
2x^2 – 3 = 15

2x^2 = 18
x^2 = 9
x = {3, -3}
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

3. Solve using the square root property:
(x + 7)^2 = 81
case 1)
(x + 7) = 9
x = 2


case 2)
(x + 7) = -9
x = -16

x = {2, -16}

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

4. Solve by completing the square:
x^2 + 8x + 2 = 0

x^2 + 8x + 2 +14= 14
(x + 4)^2 = 14
x + 4 = (+ or - )sqrt(14)
x = { -4 + sqrt(14), -4 - sqrt(14)}

Answer 4

1. x^2-6x+8=0
x^2-4x-2x+8=0
x(x-4)-2(x-4)=0
(x-2)(x-4)=0
therefore x=2,4

2. 2x^2-3=15
2x^2=18
x^2=9
x=+3 ,-3

3. (x+7)^2=81
(x+7)=+9, or (x+7)=-9
there fore x=2,-16

4. x^2+8x+2=0
x^2+2.4.x+16+2-16=0
(x+4)^2-14=0
or (x+4)=14
or (x+4)=+(root over 14) and (x+4)=-(root over 14)..
sory i dnt hve ne key 2 write root over.
Ok bro ,hpe i solve ur prob, cuz i jst finish my high school and wil b startng college so u cn gues since hw lng i havent touch them. I hpe d calculations r rite but procedure r same. Do IM me 4 ne prob.

Answer 5

x² - 6x = -8
x² - 6x + 8 = 0
(x - 4)*(x - 2) = 0
x = 4 and x = 2

2x² - 3 = 15
2x² = 18
x² = 9
x = ± 3

Now --you-- need to get busy and start solving a few of them yourself ☺

Doug

Answer 6

3. (2 + 7)^2 = 81
x = 2

Sorry, I'm only in grade 9 Math.. and I havn't done that stuff in months. But, I believe I did #3 correctly.