Question

use the square root property to find all real or imaginary solutions to the following equation. (x + 5)^2 = 49 the solution set is { }. (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any separate answers as needed.)

Explanation:

Step1: Apply square - root property

If $(x + 5)^2=49$, then $x + 5=\pm\sqrt{49}$.

Step2: Simplify the square - root

Since $\sqrt{49} = 7$, we have $x+5 = 7$ or $x + 5=-7$.

Step3: Solve for x in each case

For $x+5 = 7$, subtract 5 from both sides: $x=7 - 5=2$.
For $x + 5=-7$, subtract 5 from both sides: $x=-7 - 5=-12$.

Answer:

$\{-12,2\}$