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Which number completes the square for the expression x squared plus 14x?
AThe number 28
BThe number 49
CThe number 14
DThe number 7
Answer & Solution
Correct answer: B. The number 49
1. Completing the square adds the square of half the coefficient of x.
2. The coefficient of x here is 14, and half of 14 is 7.
3. Squaring 7 gives 49, so 49 is the number to add.
4. Adding 28 doubles instead of squaring, and the result would not factor as a perfect square.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.2 Solve Quadratic Equations by Completing the Square_
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