Question

Apply the square root property of equality:

Isolate the variable.


StartRoot (x + 9) squared EndRoot = Plus or minus StartRoot 25 EndRoot
If x + 9 = 5, then x =
.

If x + 9 = –5, then x =
.

Answer 1

yes, the correct answers are:

-4 and -14

Explanation:

got it right in edg 2020, hope this is of help :)

Answer 2

`x =-4\ or\ x = -14`

Explanation:

Given

`√(x + 9)^2 = \± √(25)`

Required

Determine the values of x

`√(x + 9)^2 = \± √(25)`

Determine the square root of 25

`√(x + 9)^2 = \± 5`

Evaluate the expression on the left hand side

`({(x + 9)}^{(1)/(2)})^2 = \± 5`

Using laws of indices

`{(x + 9)}^{(1)/(2) * 2} = \± 5`

`{(x + 9)}^(1) = \± 5`

`x + 9 = \± 5`

Split the expression into 2

`x + 9 = 5\ or\ x + 9 = -5`

Subtract 9 from both sides in both cases

`x + 9-9 = 5-9\ or\ x +9- 9 = -5-9`

`x = 5-9\ or\ x = -5-9`

`x =-4\ or\ x = -14`