16Hit1600
Advanced MathVery hardPositive solution of a quadratic in a shifted variable

Advanced Math practice question

If (x − 1)² + (x − 1) = 6 and x > 1, what is the value of x?

Answer: 3

Let u = x − 1: u² + u − 6 = (u + 3)(u − 2) = 0, so u = 2 and x = 3.

Common wrong answers

If you answered 2
2 is u, not x.
If you answered 6
6 copies the constant.
If you answered -2
−2 is x for the root u = −3, which is not greater than 1.

More Advanced Math questions

Not affiliated with the College Board. SAT is a trademark of the College Board.