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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinev2+14v+‾v^2 + 14v + \underline{\hspace{3em}}

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinev2+14v+‾v^2 + 14v + \underline{\hspace{3em}}
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the polynomial v2+14v+?v^2 + 14v + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.\newlinea=1a = 1\newlineb=14b = 14\newlinebb00
  2. Determine completion value: Determine the value needed to complete the square. To complete the square of v2+14vv^2 + 14v, add (b/2)2(b/2)^2 to the expression.\newlinePerfect square quadratic: v2+14v+(14/2)2v^2 + 14v + (14/2)^2
  3. Calculate missing number: Calculate (142)2(\frac{14}{2})^2 to find the missing number in v2+14v+v^2 + 14v + _____.\newline(142)2(\frac{14}{2})^2\newline= (7)2(7)^2\newline= 4949\newlineMissing number: 4949

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