Answer: x = 7,4
Choice A
To begin, we can get rid of the square root sign on the right side by squaring both sides of the equation. Squaring a square root will cancel out the square root, since they are opposite functions. Now we have the following:
(x-5)^2 = x-3
Now, we can expand the left side of the equation as follows:
(x-5)(x-5) = x-3
x^2 - 5x - 5x + 25 = x - 3
x^2 - 10x + 25 = x - 3
x^2 - 11x +28 = 0
Now, we can simply factor the left side of the equation as follows:
(x - 7)(x - 4) = 0
Now, we can set both expressions equal to 0 to find our solutinos:
x - 7 = 0
x = 7
x - 4 = 0
x = 4