Question

question 2 of 10 which of the following are solutions to the equation below? check all that apply. x^2 - 10x + 25 = 17 a. x = -√8 - 5 b. x = √17 + 5 c. x = √8 + 5 d. x = -√17 + 5 e. x = -√17 - 5 f. x = √17 - 5

Explanation:

Step1: Recognize perfect - square trinomial

The left - hand side of the equation $x^{2}-10x + 25$ is a perfect - square trinomial. It can be factored as $(x - 5)^{2}$, so the equation becomes $(x - 5)^{2}=17$.

Step2: Solve for x

Take the square root of both sides:
$x-5=\pm\sqrt{17}$.
Then, add 5 to both sides to isolate x:
$x = 5\pm\sqrt{17}$.
This gives two solutions: $x=\sqrt{17}+5$ and $x=-\sqrt{17}+5$.

Answer:

B. $x=\sqrt{17}+5$
D. $x =-\sqrt{17}+5$