Question

Solve (y - 4)^2 + 5 = 85, where y is a real number. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

Answer 1

To solve the equation (y - 4)^2 + 5 = 85, subtract 5, take the square root of both sides, and add 4 to get two solutions: 12.94 and -4.94.

Step-by-step explanation:

To solve the equation (y - 4)^2 + 5 = 85, where y is a real number, follow these steps:

1. Subtract 5 from both sides to isolate the squared term: (y - 4)^2 = 80.
2. Take the square root of both sides: y - 4 = ±√80.
3. Since √80 is approximately 8.9443, the equation becomes y - 4 = ± 8.9443.
4. Add 4 to both results of the square root to solve for y: y ≈ 4 ± 8.9443.

Therefore, there are two solutions:

• y ≈ 4 + 8.9443 = 12.9443 (rounded to 12.94)
• y ≈ 4 - 8.9443 = -4.9443 (rounded to -4.94)

The rounded answers are 12.94 and -4.94, which should be separated by a comma.