Question

Which of the following are solutions to the equation below?

Check all that apply.
x² + 10x + 25 = 8
□ A. x=8+ √5
B. x= √17-10
c. x=-2√√2-5
□ D. x=8-√5
E. x= -√17-10
F. X= 2√√2-5

Answer 1

The quadratic equation x² + 10x + 25 = 8 is a perfect square trinomial that simplifies to (x + 5)² = 8. After taking the square root of both sides, x = -5 ± √8 are the solutions

Step-by-step explanation:

To find the solutions to the given quadratic equation x² + 10x + 25 = 8, we first bring all terms to one side to set the equation to zero: x² + 10x + 17 = 0. The quadratic equation in the form ax²+bx+c = 0 can be solved using the quadratic formula, x = (-b ± √(b² - 4ac))/(2a).

It appears the given equation is a perfect square trinomial, as (x + 5)² = x² + 10x + 25. After adjusting for the 8 moved to the left side, we have (x + 5)² - 8 = 0. Taking the square root of both sides, we find the solutions: x = -5 ± √8.

The solutions presented are variously incorrect. Let's check each provided solution to confirm non-equivalence:

1. x = 8 + √5 is not a correct solution.
2. x = √17 - 10 is not a correct solution.
3. x = -2√√2 - 5 is not a correct solution.
4. x = 8 - √5 is not a correct solution.
5. x = -√17 - 10 is not a correct solution.
6. x = 2√√2 - 5 is not a correct solution.