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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineq2+4q+____q^2 + 4q + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineq2+4q+____q^2 + 4q + \_\_\_\_
  1. Identify values: Identify the values of aa, bb, and cc in the polynomial q2+4q+?q^2 + 4q + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.\newlinea=1a = 1\newlineb=4b = 4\newlinec=?c = ?
  2. Determine completion: Determine the value needed to complete the square. To complete the square of q2+4qq^2 + 4q, add (b/2)2(b/2)^2 to the expression.\newlinePerfect square quadratic: q2+4q+(4/2)2q^2 + 4q + (4/2)^2
  3. Calculate missing number: Calculate (42)2(\frac{4}{2})^2 to find the missing number in q2+4q+q^2 + 4q + _____.\newline(42)2(\frac{4}{2})^2\newline=(2)2= (2)^2\newline=4= 4\newlineMissing number: 44

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