Advanced MathEasy–MediumIsolating a squared term
Advanced Math practice question
If x² + 5 = 30, which of the following gives all possible values of x?
- A. 5 and −5Correct
- B. 5 only
- C. 25 and −25
- D. √35 and −√35
Answer: A. 5 and −5
Subtract 5 first: x² = 25. Two numbers square to 25, so x = 5 or x = −5. Check: 25 + 5 = 30 either way.
Why the other answers are wrong
- B. 5 only
- −5 also works, since (−5)² = 25. A square root in an equation gives both signs.
- C. 25 and −25
- 25 is x², not x. Take the square root: ±5.
- D. √35 and −√35
- √35 comes from adding 5 to 30 instead of subtracting it. Isolate x² by taking 5 away: x² = 25.
More Advanced Math questions
- Easy–Medium
If f(x) = 2x² − 3, what is f(4)? - Easy–Medium
Which expression is equivalent to (2x³)(3x⁴)? - Easy–Medium
What are the solutions to x² − 16 = 0? - Easy–Medium
Which expression is equivalent to (x + 5)²? - Easy–Medium
For x ≠ 0, which expression is equivalent to (x² + 3x) / x? - Easy–Medium
What are the solutions to the equation 2(x − 3)² − 32 = 0 ?
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