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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineq2−12q+‾q^2 - 12q + \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.\newlineq2−12q+‾q^2 - 12q + \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): −12-12\newlineConstant (cc): ??
  2. Complete the square: Determine the value needed to complete the square.\newlineTo complete the square for q2−12qq^2 - 12q, add (−122)2\left(-\frac{12}{2}\right)^2.\newlinePerfect square quadratic: q2−12q+(−122)2q^2 - 12q + \left(-\frac{12}{2}\right)^2
  3. Calculate missing value: Calculate (−12/2)2(-12/2)^2 to find the missing value in q2−12q+___q^2 − 12q + \_\_\_. \newline(−12/2)2(-12/2)^2\newline=(−6)2= (-6)^2\newline=36= 36

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