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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineq2−2q+‾q^2 - 2q + \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.\newlineq2−2q+‾q^2 - 2q + \underline{\hspace{2em}}
  1. Identify Values: Identify the values of aa, bb, and cc in the polynomial q2−2q+_q^2 − 2q + \_\_\_\_\_.\newlineComparing q2−2q+?q^2 − 2q + ? with the standard quadratic form ax2+bx+cax^2 + bx + c, we find:\newlinea=1a = 1\newlineb=−2b = -2\newlinec=?c = ?
  2. Determine Completion Value: Determine the value needed to complete the square.\newlineTo complete the square for the expression q2−2qq^2 - 2q, we add (b/2)2(b/2)^2.\newlineIn this case, b=−2b = -2, so we calculate (−2/2)2(-2/2)^2.
  3. Perform Calculation: Perform the calculation to find the missing number.\newline(−22)2=(−1)2=1(-\frac{2}{2})^2 = (-1)^2 = 1\newlineThe missing number to complete the square is 11.

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