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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlined2−6d+_____d^2 - 6d + \_\_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlined2−6d+_____d^2 - 6d + \_\_\_\_\_
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the polynomial d2−6d+?d^2 − 6d + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.\newlinea=1a = 1\newlineb=−6b = -6\newlinebb00
  2. Calculate (b2)2(\frac{b}{2})^2: To complete the square, we need to add (b2)2(\frac{b}{2})^2 to the polynomial d2−6dd^2 − 6d. Calculate (b2)2(\frac{b}{2})^2 using the value of b from the previous step.\newline(−62)2=(−3)2=9(-\frac{6}{2})^2 = (-3)^2 = 9
  3. Complete the square: The number that completes the square is 99. The polynomial becomes a perfect-square quadratic when we add this number: d2−6d+9d^2 - 6d + 9.

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