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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlineg2+18g+‾g^2 + 18g + \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.\newlineg2+18g+‾g^2 + 18g + \underline{\hspace{2em}}
  1. Identify values: Identify the values of aa, bb, and cc in the polynomial g2+18g+?g^2 + 18g + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.\newlinea=1a = 1\newlineb=18b = 18\newlinec=?c = ?
  2. Calculate square completion: To complete the square for the polynomial g2+18gg^2 + 18g, we need to add (b2)2(\frac{b}{2})^2 to it.\newlineCalculate (182)2(\frac{18}{2})^2 to find the value that completes the square.\newline(182)2=(9)2=81(\frac{18}{2})^2 = (9)^2 = 81
  3. Complete the square: The number that completes the square is 8181, so the polynomial becomes a perfect-square quadratic when we add 8181. The completed square form is g2+18g+81g^2 + 18g + 81.

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