Question

The first question: Solve by taking the square root I need help understanding the steps to solve this!

The second one: Solve by completing the square I also need help understanding how to solve this​

Answer 1

see explanation

Explanation:

(1)

Given

3(x + 3)² - 1 = - 13 ( add 1 to both sides )

3(x + 3)² = - 12 ( divide both sides by 3 )

(x + 3)² = - 4 ( take the square root of both sides )

x + 3 = ±
`√(-4)` = ± 2i ( subtract 3 from both sides )

x = - 3 ± 2i ← complex conjugate roots

(2)

Given

3x² - 12x + 27 = 0 ( subtract 27 from both sides )

3x² - 12x = - 27 ( divide through by 3 )

x² - 4x = - 9

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = - 9 + 4

(x - 2)² = - 5 ( take the square root of both sides )

x - 2 = ±
`√(-5)` = ± i
`√(5)` ( add 2 to both sides )

x = 2 ± i
`√(5)` ← complex conjugate roots