Question

Which of the following are solutions to the equation (5x + 1)^2 = 7?

A) x = √6
B) x = -√7 - 1/5
C) x = -1
D) x = -√5
E) x = -√7
F) x = -√6

Answer 1

The solution to the equation (5x + 1)^2 = 7 is found by taking the square root of both sides and solving for x, which results in x = (-√7 - 1)/5, matching option B.

Step-by-step explanation:

To find the solutions to the equation (5x + 1)^2 = 7, we start by taking the square root of both sides of the equation, which gives us two possible equations:

• 5x + 1 = √7
• 5x + 1 = -√7

Solving the first equation for x yields:

• 5x = √7 - 1
• x = ( √7 - 1)/5

Solving the second equation for x gives us:

• 5x = -√7 - 1
• x = (-√7 - 1)/5

After simplifying, we can see that the solutions are:

• x = (√7 - 1)/5, which is not listed among the options
• x = (-√7 - 1)/5, which matches option B

Therefore, the solution to the equation is option B: x = -√7 - 1/5.