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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinex2+20x+‾x^2 + 20x + \underline{\hspace{1cm}}

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinex2+20x+‾x^2 + 20x + \underline{\hspace{1cm}}
  1. Identify Values: Identify the values of aa, bb, and cc in the quadratic expression.\newlineLeading coefficient (aa): 11\newlineCoefficient of linear term (bb): 2020\newlineConstant (cc): ?
  2. Determine Completion: Determine the value needed to complete the square.\newlineTo complete the square for x2+20xx^2 + 20x, add (b/2)2(b/2)^2.\newlinePerfect square quadratic: x2+20x+(20/2)2x^2 + 20x + (20/2)^2
  3. Calculate Missing Value: Calculate (20/2)2(20/2)^2 to find the missing value in x2+20x+‾x^2 + 20x + \underline{\hspace{1em}}.$20/2)2\$20/2)^2=102= 10^2=100= 100The missing value is 100100.

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