Question

Can you check the following problems?

4. x^2 - 10x +25 = 9
x^2 - 10x + (25 -9) = 9 - 9
x^2 - 10x + 16 = 0
(x - 8)(x-2) = 0
x - 8 = 0, x - 2 = 0
x = 8, x = 2

5. x^2 - 6x + 9 = 49
x^2 - 6x + ( 9 - 49) = 49 - 49
x^2 - 6x - 40 = 0
(x -10)(x + 4) = 0
x - 10 = 0, x +4 = 0
x = 10, x = -4

6. x^2 + 2x + 1 = 64
x^2 + 2x + (1 - 64) = 64 - 64
x^2 + 2x -63 = 0
(x +9)(x - 7) = 0
x + 9 = 0, x - 7 = 0
x = -9, x = 7

7. x^2 - 18x + 81 = 24
x^2 - 18x + (81 - 24) = 24 - 24
x^2 - 18x + 57 = 0
(x - 19)(x - 3)
Not sure what to do next. 3 & 19 doesnt give 18 for middle term.

8. x^2 + 12x + 36 = 75
x^2 + 12x + (36 - 75) = 75 -75
x^2 + 12x - 39 = 0
Not sure what's next. 3 & 13 doesn't give 12 for middle term.

I'm not about these below either.
9. (x - 1/2)^2 = 1
√(x - 1/2)^2 = +- √1
x - 1/2 = +- 1
x - 1/2 = 1, x -1/2 = -1
x = 3/2, -1/2

10. (x - 3/2)^2 = 7/4
√(x - 3/2)^2 = +- √7/√4
x - 3/2 = +- √7/2
x - 3/2 = +- √7/2
x = 3/2 +- √7/2 or
x = (3 +- √7)/2

11. (x + 5/2)^2 = 15/4
√(x + 5/2)^2 = +- √15/√4
x + 5/2 = +- √15/2
x = -5/2 +- √15/2 or
x = (-5 +- √15)/2

12. 2x^2 = 5
2x^2/2 = 5/2
x^2 = 5/2
√x^2 = +- √5/√2
x = +- √5/√2

13. (x - 1/2)^2 = 3/2
√(x - 1/2)^2 = +- √3/√2
x - 1/2 = +- √3/2
x = 1/2 +- √3/√2

14. (x-3/5)^2 = 4/5
√(x - 3/5)^2 = +- √4/√5
x - 3/5 = 2√5
x = 3/5 +- 2√5 or
x = (3 +- 2√5)/5

15. 3(x + 7/3)^2 = 1
[3(x + 7/3)^2)]/3 = 1/3
(x + 7/3)^2 = 1/3
√(x + 7/3)^2 = +- √1/√3
x + 7/3 = +- √3
x = -7/3 +- √3 or
x = (-7 +- √3)/3

Answer 1

#7: x^2 - 18x + 57 = 0
Looks like the quadratic formula is what you'll need:

x = 9±√24

Or, you could complete the square, as was done in the following problems:

x^2 - 18x + 57 = 0
x^2 - 18x + 81 = 24
(x-9)^2 = ±√24
x = 9±√24

The rest look good, except for a few typos.

Answer 2

Okay. thanks! It was confusing to me. I'll double check them for typos and look up quadratic formula.