Advanced Math practice question

Answer: 9

Square both sides: x + 7 = (x − 5)² = x² − 10x + 25. Rearrange: x² − 11x + 18 = 0, which factors as (x − 2)(x − 9) = 0, so x = 2 or x = 9. Now check each in the ORIGINAL equation. x = 9: √16 = 4 and 9 − 5 = 4, true. x = 2: √9 = 3 but 2 − 5 = −3, false. So the only solution is 9.

Common wrong answers

If you answered 2

2 comes out of the squared equation but fails the original: √(2 + 7) = 3, while 2 − 5 = −3. Squaring can create solutions that weren't there — always check.

If you answered 11

11 is the sum of the two candidates from the factored equation, not a solution. Solve (x − 2)(x − 9) = 0 and then test each value.

If you answered 18

18 is the constant in x² − 11x + 18 = 0, not a solution. Factor it and test the candidates in the original equation.

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