Question

Hwo do I solve this equation?

Answer 1

:

Answer: n = - 1

Explanation:

square both sides

()² = (n + 3)² ← expand factors

4n + 8 = n² + 6n + 9

rearrange into standard form : an² + bn + c = 0 : a ≠ 0

subtract 4n + 8 from both sides

n² + 2n + 1 = 0

(n + 1)² = 0 ⇒ n + 1 = 0 ⇒ n = - 1

As a check, substitute n = - 1 into the equation and if both sides are equal then it is the solution.

left side = = = 2

right side = - 1 + 3 = 2

Hence n = - 1 is the solution

Answer 2

n = - 1

Explanation:

square both sides

(
`√(4n+8)`)² = (n + 3)² ← expand factors

4n + 8 = n² + 6n + 9

rearrange into standard form : an² + bn + c = 0 : a ≠ 0

subtract 4n + 8 from both sides

n² + 2n + 1 = 0

(n + 1)² = 0 ⇒ n + 1 = 0 ⇒ n = - 1

As a check, substitute n = - 1 into the equation and if both sides are equal then it is the solution.

left side =
`√(-4+8)` =
`√(4)` = 2

right side = - 1 + 3 = 2

Hence n = - 1 is the solution