Question

use the square root property to find all real or imaginary solutions to the following equation. (x + 7)^2 = 16 the solution set is {}. (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in separate answers as needed.)

Explanation:

Step1: Apply square - root property

Take the square root of both sides of the equation $(x + 7)^2=16$. We get $x + 7=\pm\sqrt{16}$.

Step2: Simplify the right - hand side

Since $\sqrt{16}=4$, the equation becomes $x + 7=\pm4$.

Step3: Solve for x in two cases

Case 1: When $x + 7 = 4$, subtract 7 from both sides: $x=4 - 7=-3$.
Case 2: When $x + 7=-4$, subtract 7 from both sides: $x=-4 - 7=-11$.

Answer:

$\{-11,-3\}$