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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2−26f+‾f^2 - 26f + \underline{\hspace{2em}}

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Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2−26f+‾f^2 - 26f + \underline{\hspace{2em}}
  1. Identify coefficients: Identify the values of aa, bb, and cc in the polynomial f2−26f+?f^2 − 26f + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.a=1a = 1b=−26b = -26c=?c = ?
  2. Calculate half and square: To complete the square, we need to add the square of half of the coefficient of ff, which is b2\frac{b}{2}, to the polynomial.\newlineHalf of −26-26 is −262=−13-\frac{26}{2} = -13.\newlineNow square −13-13 to get (−13)2(-13)^2.
  3. Find missing number: Calculate (−13)2(-13)^2 to find the number that completes the square.\newline(−13)2=169(-13)^2 = 169\newlineSo, the missing number is 169169.

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