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ASVAB · Algebra Basics and Equations

If x² = 49, what are the possible values of x?

Reviewed by Jordan Morley, Editorial Lead at 247SimpleTests. Written by the 247SimpleTests Editorial Team from the official source material cited on every question.

Correct answer

7 and −7

  1. A 24.5
  2. B 7 only
  3. C 7 and −7
  4. D ±49

Why this is the answer

If x² = 49, then x = ±7 (both 7 AND −7), because 7² = 49 AND (−7)² = 49. ASVAB Mathematics Knowledge tests square roots and equations.

Key concept: when solving x² = a number, there are usually TWO solutions — a positive and a negative root — because squaring a negative number gives a positive result.

Common error: giving only the positive root (7). The square root symbol √ alone denotes the positive root, but solving the EQUATION x² = 49 yields both +7 and −7. Check: (−7)² = (−7)(−7) = 49. ✓

Source: ASVAB Mathematics Knowledge — Square Roots / Quadratics

Practice more questions

This question is from our ASVAB Practice Tests practice test. Take the full practice test to test your knowledge across all Algebra Basics and Equations and other topics.

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About this topic: Algebra Basics and Equations

Algebra basics cover solving linear equations and inequalities, working with expressions, substitution and simple systems. Do the same operation to both sides, and check your answer by substituting it back. This is one of 17 Mathematics Knowledge questions on algebra basics and equations, each with a full explanation on a single study page.

New to this exam? Our ASVAB exam guide explains the format, scoring, and how to prepare.

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