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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2−6f+_____f^2 - 6f + \_\_\_\_\_

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Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2−6f+_____f^2 - 6f + \_\_\_\_\_
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the polynomial f2−6f+f^2 − 6f + _____.\newlineComparing f2−6f+?f^2 − 6f + ? with the standard quadratic form ax2+bx+cax^2 + bx + c, we find:\newlinea=1a = 1\newlinebb00\newlinebb11
  2. Determine completion value: Determine the value needed to complete the square.\newlineTo complete the square for the expression f2−6ff^2 − 6f, we need to add (b/2)2(b/2)^2.\newlineIn this case, b=−6b = -6, so we calculate (−6/2)2(-6/2)^2.
  3. Perform calculation: Perform the calculation to find the missing number.\newline(−62)2=(−3)2=9(-\frac{6}{2})^2 = (-3)^2 = 9\newlineThe missing number that completes the square is 99.

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