complete the work shown to find a possible solution of the equation.\n$(x - 5)^{\frac{1}{2}} + 5 = 2$\n$(x…

complete the work shown to find a possible solution of the equation.\n$(x - 5)^{\frac{1}{2}} + 5 = 2$\n$(x - 5)^{\frac{1}{2}} = -3$\n$left(x - 5)^{\frac{1}{2}}\right^2 = (-3)^2$\na possible solution of the equation is \\boxed{}.

complete the work shown to find a possible solution of the equation.\n$(x - 5)^{\frac{1}{2}} + 5 = 2$\n$(x - 5)^{\frac{1}{2}} = -3$\n$left(x - 5)^{\frac{1}{2}}\right^2 = (-3)^2$\na possible solution of the equation is \\boxed{}.

Answer

Explanation:

Step1: Simplify the left side

Using the exponent rule ((a^m)^n = a^{mn}), for (\left[(x - 5)^{\frac{1}{2}}\right]^2), we get (x - 5) (since (\frac{1}{2}\times2 = 1)).

Step2: Simplify the right side

Calculate ((-3)^2), which is (9) (because squaring a negative number gives a positive result).

Step3: Solve for (x)

Now we have the equation (x - 5 = 9). Add (5) to both sides of the equation: (x=9 + 5).

Step4: Calculate the value of (x)

(9+5 = 14), so (x = 14). We should check if this solution is valid by plugging it back into the original equation: ((14 - 5)^{\frac{1}{2}}+5=\sqrt{9}+5 = 3 + 5 = 8\neq2). Wait, but the problem says "a possible solution" (even though it's extraneous, we follow the steps). The steps led us to (x = 14) from the algebraic manipulation.

Answer:

(14)