Advanced MathHardValue of x from a difference of squared binomials
Advanced Math practice question
For what value of x is (2x − 5)² − (2x + 5)² equal to −120?
Answer: 3
Expand: (4x² − 20x + 25) − (4x² + 20x + 25) = −40x. So −40x = −120 and x = 3. (Shortcut: a² − b² = (a − b)(a + b) with a = 2x − 5 and b = 2x + 5 gives (−10)(4x) = −40x.)
Common wrong answers
- If you answered 6
- 6 comes from −20x = −120, subtracting only one of the two 20x terms.
- If you answered -3
- −3 has the wrong sign: −40x = −120 gives x = 3.
- If you answered 2.4
- 2.4 comes from −50x = −120, wrongly keeping the constants in the difference.
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