Part 1Solve by using the square root property.(xminus−77)squared2equals=6464 Part 1The solution(s) is(are) x = [input]enter your response here .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

Question

Part 1Solve by using the square root property.​(xminus−77​)squared2equals=6464 Part 1The​ solution(s) is(are) x​ = [input]enter your response here .​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​ needed.)

BlackTom AI · Accepted Answer

The problem asks to solve by using the square root property for the equation (x - 77)^2 = 64, and then to enter the solution(s) as integers.
First, recognize the square on the left side: when something is squared equals a number, we can take the square root of both sides to get the base with a ± sign. So we apply the square root property to (x - 77)^2 = 64.
Next, take the square root of both sides: x - 77 = ±√64. Since √64 = 8, this gives two possibilities: x - 77 = 8 or x - 77 = -8.
Proceed by solving each linear equation:
- If x - 77 = 8, then x = 77 + 8 = 85.
- If x - 77 = -8, then x = 77 - 8 = 69.
A quick consistency check is to substitute back into the original equation to ensure both satisfy the squared form. For x = 85, (85 - 77)^2 = 8^2 = 64, which matches the right-hand side. For x = 69, (69 - 77)^2 = (-8)^2 = 64, which also matches.
Note on possible confusion: if the right-hand side were actually 6464 as written in some garbled text, its square root would be 8√101, which would lead to non-integer solutions and would not yield clean integers like 69 and 85. The clean integer results arise specifically from recognizing 64 as the right-hand side, i.e., √64 = 8 and respecting the ±8 from the square root property.
Therefore, the process yields two solutions corresponding to adding or subtracting 8 from 77, namely 69 and 85.

Part 1Solve by using the square root property.(xminus−77)squared2equals=6464 Part 1The solution(s) is(are) x = [input]enter your response here .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)多项填空题

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Part 1Solve by using the square root property.​(xminus−77​)squared2equals=6464 Part 1The​ solution(s) is(are) x​ = [input]enter your response here .​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​ needed.)多项填空题