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

Answer:

$x =-4\ or\ x = -14$

Step-by-step explanation:

Given

$\sqrt{x + 9}^2 = \± \sqrt{25}$

Required

Determine the values of x

$\sqrt{x + 9}^2 = \± \sqrt{25}$

Determine the square root of 25

$\sqrt{x + 9}^2 = \± 5$

Evaluate the expression on the left hand side

$({(x + 9)}^{\frac{1}{2}})^2 = \± 5$

Using laws of indices

${(x + 9)}^{\frac{1}{2} * 2} = \± 5$

${(x + 9)}^{1} = \± 5$

$x + 9 = \± 5$

Split the expression into 2

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

Subtract 9 from both sides in both cases

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

$x = 5-9\ or\ x = -5-9$

$x =-4\ or\ x = -14$

Answer 2

Answer:

yes, the correct answers are:

-4 and -14

Step-by-step explanation:

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