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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+22f+‾f^2 + 22f + \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.\newlinef2+22f+‾f^2 + 22f + \underline{\hspace{2em}}
  1. Identify coefficients: Identify the values of aa, bb, and cc in the polynomial f2+22f+?f^2 + 22f + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.\newlinea=1a = 1\newlineb=22b = 22\newlinec=?c = ?
  2. Complete the square: Determine the value needed to complete the square. To complete the square of f2+22ff^2 + 22f, add (b/2)2(b/2)^2 to the expression.\newlinePerfect square quadratic: f2+22f+(22/2)2f^2 + 22f + (22/2)^2
  3. Calculate missing number: Calculate (222)2(\frac{22}{2})^2 to find the missing number in f2+22f+f^2 + 22f + _____.\newline(222)2(\frac{22}{2})^2\newline= (11)2(11)^2\newline= 121121\newlineMissing number: 121121

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