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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinek2−22k+‾k^2 - 22k + \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.\newlinek2−22k+‾k^2 - 22k + \underline{\hspace{2em}}
  1. Identify coefficients: Identify the values of aa, bb, and cc in the quadratic expression.\newlineLeading coefficient (aa): 11\newlineCoefficient of linear term (bb): −22-22\newlineConstant (cc): ??
  2. Complete the square: Determine the value needed to complete the square.\newlineTo complete the square for k2−22kk^2 - 22k, add (−222)2\left(-\frac{22}{2}\right)^2.\newlinePerfect square quadratic: k2−22k+(−222)2k^2 - 22k + \left(-\frac{22}{2}\right)^2
  3. Calculate missing value: Calculate (−22/2)2(-22/2)^2 to find the missing value in k2−22k+___k^2 − 22k + \_\_\_.\newline(−22/2)2(-22/2)^2\newline=(−11)2= (-11)^2\newline=121= 121

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