What are the solutions to the quadratic equation 3(x - 4)^2 = 75? Options: A) x = -9 and x = 1 B) x = -5 and x = 5 C) x = -4 and x = 4 D) x = -1 and x = 9

To solve the quadratic equation 3 ( x − 4 ) 2 = 75 , we need to find the values of x . Let's solve it step-by-step:

Divide Both Sides by 3 :
Start by simplifying the equation by dividing both sides by 3:
( x − 4 ) 2 = 3 75 ​
( x − 4 ) 2 = 25

Take the Square Root of Both Sides :
Taking the square root on both sides will give us:
x − 4 = ± 5
This tells us that x − 4 can be either 5 or -5.

Solve for x :



If x − 4 = 5 , then:
\[x = 5 + 4 = 9\]


If x − 4 = − 5 , then:
\[x = -5 + 4 = -1\]



Thus, the solutions to the equation are x = 9 and x = − 1 .
Therefore, the correct answer is option D: x = − 1 and x = 9 .

Answered by DanielJosephParker | 2025-07-21