Question

Solving wuadractics with square roots.

Answer 1

`2(x+5)^(2) = 1 + 3 \iff 2(x+5)^(2) = 4 \iff (x+5)^(2) = 2`

`|x+5| = \pm √(2)`

`x + 5 = - √(2) \iff x_(1) = - √(2) - 5`

`x + 5 = √(2) \iff x_(2) = √(2) - 5`

`\implies \{- √(2) - 5, \ √(2) - 5\}`

Answer 2

x = - 5 ±
`√(2)`

Explanation:

2(x + 5)² - 3 = 1 ( add 3 to both sides )

2(x + 5)² = 4 ( divide both sides by 2 )

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

x + 5 = ±
`√(2)` ( subtract 5 from both sides )

x = - 5 ±
`√(2)`

Then

x = - 5 -
`√(2)` , x = - 5 +
`√(2)`