Final answer:
After applying the quadratic formula to the equation x^2 + 10x + 25 = 8, it is determined that none of the given options are correct solutions. The actual solutions are x = -5 + 2√2 and x = -5 - 2√2.
Step-by-step explanation:
The student is trying to find solutions to the quadratic equation x^2 + 10x + 25 = 8. To solve this equation, we can first bring all terms to one side to have zero on the other side, creating a standard quadratic equation of the form ax^2 + bx + c = 0:
x^2 + 10x + 25 - 8 = 0
x^2 + 10x + 17 = 0
This equation does not factor nicely, so we will need to use the quadratic formula to find the solutions.
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). For our equation, a = 1, b = 10, and c = 17.
Substituting the values into the quadratic formula, we get:
x = (-10 ± √(10² - 4*1*17)) / (2*1)
x = (-10 ± √(100 - 68)) / 2
x = (-10 ± √32) / 2
x = (-10 ± 4√2) / 2
x = -5 ± 2√2
So, the solutions to the equation are x = -5 + 2√2 and x = -5 - 2√2. Among the provided options, none exactly match these solutions.