Solve by extracting the square root?

Question

Show checking pls.

x^2 - 6x + 9 = 0

(5x+10)^2 + 7 = 0

Extracting the square root, don't use other methods.

Answer 1

1st problem:

x² - 6x + 9 = 0

x² - 6x = - 9

x² - 3x = - 9 + 3²

x² - 3x = - 9 + 9

(x - 3)² = 0

x - 3 = 0

x = 3

Answer: x = 3; Factors: (x - 3)² or (x - 3)(x - 3)

Proof:

3² - 6(3) = - 9

9 - 18 = - 9

- 9 = - 9

2nd problem:

(5x + 10)² + 7 = 0

25x² + 50x + 50x + 100 + 7 = 0

25x² + 100x = - 107

x² + 4x = - 107/25

x² + 2x = - 107/25 + 2²

x² + 2x = - 107/25 + 100/25

(x + 2)² = - 7/25

x + 2 = √(- 7/25)

1st value of x:

x = - (√[7/25]) - 2

2nd value of x:

x + 2 = √(7/25)

x = (√[7/25]) - 2

Answer: x = (√[7/25]) - 2, - (√[7/25]) - 2

Answer 2

x² - 6x + 9 = 0

(x - 3)² = 0

x - 3 = ± √0

x = 3 ± 0

x = 3

(5x+10)² + 7 = 0

(5x + 10)² = -7

5x + 10 = ± √(-7)

5x = -10 ± i√7

x = -2 ± (i√7) / 5

Answer 3

x^2-6x+9=0

x^2-[2*x*3]+(3)^2=0

(x-3)^2=0

x-3=0

x=3

(5x+10)^2+7=0

25x^2 +100+2*5x*10+7=0

25x^2+107+100x=0