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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineq2−28q+‾q^2 - 28q + \underline{\hspace{2em}}

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineq2−28q+‾q^2 - 28q + \underline{\hspace{2em}}
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic expression q2−28q+?q^2 - 28q + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1
    b=−28b = -28
    c=?c = ?
  2. Calculate square: To complete the square, we need to add the square of half of the coefficient of qq, which is b2\frac{b}{2}, to the expression. Calculate (−282)2\left(-\frac{28}{2}\right)^2.(−282)2=(−14)2=196\left(-\frac{28}{2}\right)^2 = (-14)^2 = 196
  3. Complete the square: The number that completes the square is 196196. So the expression becomes q2−28q+196q^2 - 28q + 196, which is a perfect square quadratic.

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