Verified answer

Answer:

Step-by-step explanation:

1. x² - 36 = 0

Transpose

x² = 36

Extract the square root

√x² = √36

x = 6

x = -6

2. (4-5)² = 25   ---------no variable unable to solve

3. 16x² - 3x = 0

Get the factors of the terms

x(16x -3) = 0

x = 0

16x - 3 = 0

16x = 3

x = 3/16

4. y² - y - 12 = 0

Factor

(y -4)(y + 3) = 0

y - 4 = 0

y = 4

y + 3 = 0

y = -3

5. m² + 2m - 8 = 0

m² + 2m + 1 - 8 -1 = 0

(m + 1)² - 9 = 0

(m + 1)² = 9

Get the square root for each side of the equation

√(m+1)² = √9

m + 1 = +-3

m + 1 = 3

m = 3 - 1

m = 2

m+1 = -3

m = -3 -1

m = -4

6. n² + 10n - 75 = 0

10/2 = 5

5²

n² + 10n +5² - 75 -5² = 0

(n +5)² - 75 - 25 = 0

(n +5)² = 75 +25

Get the square root

√(n+5)² = √100

n + 5 = +-10

n + 5 = 10

n = 10 -5

n = 5

n + 5 = -10

n = -10 - 5

n = -15

7. x² + 6x + 5 = 0

Use quadratic formula

[tex]x = \frac{-b (+-)\sqrt{b^2-4ac} }{2a}[/tex]

a = 1

b = 6

c = 5

[tex]x = \frac{-6(+-) \sqrt{6^2-4(1)(5)} }{2(1)} \\x = \frac{-6 (+-) \sqrt{36-20} }{2} \\x = \frac{-6(+-)\sqrt{16} }{2}\\ x = \frac{-6(+-)4}{2} \\x = \frac{-6+4}{2}\\ x = \frac{-2}{2} \\x = -1\\x = \frac{-6-4}{2}\\ x = \frac{-10}{2} \\x = -5\\[/tex]

x = -1

x = -5

8. x² - 2x + 1 = 0

a = 1

b = -2

c = 1

[tex]x = \frac{-(-2)(+-)\sqrt{(-2)^2 - 4(1_)1)} }{2(1)} \\x = \frac{2(+-)\sqrt{4-4} }{2} \\x = \frac{2}{2} \\x = 1[/tex]

x = 1